Quantifying Antiquity Veritas in Numeris

Quantifying Antiquity — ramp planking and the timber bill

1,204 Shipload Equivalents; 602 Literal Imported Shiploads

The timber would have needed to be procured, transported, converted, installed, and replaced as it wore out. This page follows that material requirement throughout the build.

The Palermo Stone records forty ships carrying cedar. The model requires enough timber to fill about 1,204 such shiploads over twenty years: about 1,164 more than that recorded delivery.

That is all the timber, not just imported cedar. Even after allowing half to come from local trees, about 602 shiploads would still have had to arrive from abroad. The trees would have had to be felled, moved, cut into usable wood, and installed. As the planks wore out, that work would have had to be repeated.

Workbook figures carry cell addresses and badges. Underlined figures are drawn dimensions. SOURCE a pinned source ASSUMPTION a chosen value DERIVED computed LIVE model-linked POLICY ruling

Timber, raw to usable 1 / 6 The chain

Screen 1 of 6

Raw timber is not usable timber yet.

Here, felled means the raw timber that has to be cut and procured before losses. Some of that timber is lost in transit and storage. What survives is converted into usable members, and a share of that is rejected for species, dimension or defect.

The whole page turns on the gap between the two ends of that chain. Raw timber is what must be procured and delivered. Installed timber is what survives the loss chain and actually goes into service. On the model's own loss rates they differ by a factor of 2.59.

A solid narrowing through four loss stages, from 100 cubic meters raw timber to 38.61 installed A block whose height is proportional to volume starts at 100 cubic meters raw timber, also called felled timber, and steps down four times: 12 per cent water damage, 10 per cent handling and transport, 25 per cent structural reject, and 35 per cent conversion. What remains is 38.61 cubic meters installed. A double-headed arrow at the right marks the ratio between the raw timber height and the installed height as 2.59 times. 100 m³ RAW TIMBER, STEPPED DOWN TO WHAT GOES INTO SERVICE 100 m³ 88 m³ 79.2 m³ 59.4 m³ 38.61 m³ 12% water damage Inputs_03!B176 10% handling and transport Inputs_03!B144 25% structural reject Inputs_03!B143 35% conversion Inputs_03!B142 RAW / FELLED raw log volume that must be procured after rot, warp, river soak after breakage, transit and staging after species, size, defect, grade INSTALLED what goes into service and wears out 2.59×

Height is proportional to volume; the widths of the segments carry no meaning. The four rates are applied one after another, not added — 0.88 × 0.90 × 0.75 × 0.65 leaves 38.61% of what was felled. Because they multiply, the order they are shown in is presentational: any order gives the same 38.61%. All four are levers the workbook labels Assumption, and the worked example above is the register's own, at their current settings (MethodsRulings_48 rows 9–19).

What survives the chain

Combined usable yield 38.61%WoodFuelCredit_44!B9Derived. Turn it round and 100 m³ of planking in service needs 259 m³ felled to produce it. Everything the rest of this page counts is counted at the felled end.

Why the felled end

Ruling MR-07, MethodsRulings_48Policy. The comparator this page uses is cedar that arrived on ships, counted as it arrived. So the numerator has to be raw timber as it must arrive. Log against log.

The conversion loss lands after delivery

Inputs_03!B142 covers "rough-log or imported beam volume to usable structural member" — imported wood carries the 35% conversion loss too, once it is here. That is the cell that decides the whole basis, and it is an Assumption.

Screen 2 of 6

The ramps do not hold timber. They consume it.

Ramp planking is a wear stream, not a standing stock. At any one moment there is very little timber on the ramps. Over twenty years of sledge traffic there is an enormous amount of timber gone through them.

The traffic is not this model's estimate. It is the published dataset of the ramp study this sheet tests: 2,236,463 blocksIERRampTimber_38!B5Source moved over 670,264 loaded sledge-kmIERRampTimber_38!B6Source of ramp surface, empty returns excluded.

A length of planked ramp lane, and a stock-versus-throughput ledger for ramp planking On the left, a plan of a 3.8 meter wide ramp lane with planking covering 30 per cent of the running surface, and a small section showing the plank thickness. On the right, the 166 cubic meters standing on the ramps at any one moment is shown as a small stock marker. Beneath it, the 26,743.5 cubic meters installed and replaced over the build is drawn as a flow bar, and the 69,265.8 cubic meters felled to yield it is drawn as a larger proportional bar. THE LANE — 3.8 m WIDE STOCK VERSUS THROUGHPUT 3.8 m 14 m of lane, drawn planking covers 30% of the running surface IERRampTimber_38!B17 0.07 m plank, in section IERRampTimber_38!B18 thickness drawn at 10×, or it would be a line every 2,000 loaded passes, one lane-meter of planking is spent IERRampTimber_38!B19 · service life, ASSUMPTION 335,132 replacement events over the build — B24 AT ONE MOMENT the ramps hold very little timber at once 166.0 m³ ON RAMPS AT ONCE IERRampTimber_38!B28 + B29 OVER TWENTY YEARS wear turns the small stock into repeated replacement 26,743.5 m³ INSTALLED / REPLACED IERRampTimber_38!B26 335,132 lane-meter replacement events accumulate into this installed flow IERRampTimber_38!B24 RAW TIMBER REQUIRED Screen 1's loss chain turns installed volume into procurement volume 2.59× installed 69,265.8 m³ FELLED / PROCURED IERRampTimber_38!B30 one line scale: 400 px = 69,265.8 m³

Two scales, each stated. The lane is drawn at 26 pixels to the meter, with plank thickness alone stretched ten times so it is visible. The right-hand ledger uses one line scale for the two volume bars; the small standing-stock marker above them is a label for the at-one-moment quantity, not a same-scale bar. The point is throughput, not footprint. Standing stock is the sum of two cells, lanes 92.5 m³IERRampTimber_38!B28Derived and corner bays 73.5 m³IERRampTimber_38!B29Derived.

The recycling answer is true, and it answers the wrong thing

The usual reply to ramp timber is that the planking was lifted, moved up and reused, so its footprint is effectively nothing. Of the standing stock, that is correct. Under 170 m³ is on the ramps at once, and reuse is exactly what keeps it that low.

Reuse is the denominator. Wear is the numerator. Planking abraded away under 670,264 loaded sledge-km does not come back into service, and it is that abraded volume — 26,743.5 m³IERRampTimber_38!B26Derived installed over the build, 69,265.8 m³IERRampTimber_38!B30Derived felled to yield it — that has to be cut, carried and converted again.

The wear stream is what the ramp study calls minor maintenance (IERRampTimber_38!E26). This page does not say the recycling claim is false. It says the claim is about the standing stock and has no bearing on the wear.

Where the wear number comes from

335,132IERRampTimber_38!B24Derived lane-meter replacement events: the loaded passes divided by a plank service life of 2,000 passesIERRampTimber_38!B19Assumption. Each event costs 0.0798 m³IERRampTimber_38!B25Derived — lane width by planked share by thickness.

The steelman on plank life, and exactly how far it gets The workbook carries a service-life multiplier at Inputs_03!B192Assumption, which credits flipping and down-grading worn planks before discard. Set to 2.0 it halves this wear stream to 1,731.6 m³/yrTimberLabor_40!B37Derived and the whole timber bill to 2,398.8 m³/yrTimberLabor_40!B38Derived. It is set to 1, so every other figure on this page is on the un-credited basis. On that steelmanned basis the annual comparison on screen 4 does not survive. A year needs 34.96 shiploadsTimberLabor_40!B39Derived, which is 0.87×TimberLabor_40!B40Derived the record — it falls below forty ships. The build-long comparison does survive: 699.1 shiploadsTimberLabor_40!B42Derived over twenty years, 17.48×TimberLabor_40!B43Derived the record. The workbook says so in its own note: lead with the annual figure at the default and the build-long figure under the steelman (TimberLabor_40!E39, E43). And the 2,000-pass life it doubles is already generous, sitting on top of a chocking and dunnage system the model does not count at all (IERRampTimber_38!A45Policy).

Screen 3 of 6

Two different timber streams. One is more than five times the other.

The subtotal most readers meet first is the structural and support timber screen: sleds, levers, cribbing, anchors, workshops, boats, and other reusable project stock. The separate ramp-planking wear stream is more than five times larger than that subtotal.

Treating the structural/support subtotal as the whole timber bill omits the ramp-planking wear stream, understates the bill by a factor of six, and is the single most likely accounting error in this work.

The timber bill as proportional material geometry A proportional annual timber unit is split into 667.2 cubic meters of structural timber and 3,463.3 cubic meters of ramp planking, for 4,130.5 cubic meters per year. The same annual unit is repeated twenty times in a five by four field, representing 82,609.5 cubic meters over the build. The structural portions are then assembled as their own quantity and compared with the complete requirement, showing that the full requirement is 6.19 times the structural subtotal. Barge hull timber is drawn as a small separate sliver outside the total. ONE SCALE THROUGHOUT: ANNUAL UNIT, TWENTY-YEAR FIELD, STRUCTURAL SUBTOTAL. YEARLY TIMBER REQUIREMENT — 4,130.5 m³ TimberLabor_40!B7 STRUCTURAL 667.2 m³/yr RAMP PLANKING — 3,463.3 m³/yr 5.19× structural timber RAMP PLANKING = 5.19× STRUCTURAL TIMBER BARGE-HULL TIMBER 80.6 m³/yr outside total above TimberLabor_40!B8 TWENTY-YEAR TIMBER REQUIREMENT — 82,609.5 m³ TimberLabor_40!B27 twenty identical annual units, each preserving the 667.2 / 3,463.3 split STRUCTURAL TIMBER ONLY — 13,343.7 m³ TimberSystem_31!B38 FULL REQUIREMENT = 6.19× ACTUAL TIMBER REQUIREMENT — 82,609.5 m³ TimberLabor_40!B27 69,265.8 m³ ramp planking is omitted if the structural subtotal is treated as total

Everything here is at one scale. The yearly unit is drawn once, then repeated twenty times. The structural/support pieces are a valid subtotal, but the comparison shows why they cannot be read as the timber bill: the complete requirement is 6.19 times larger, and the omitted ramp-planking volume is 69,265.8 m³. Both streams are counted on the felled basis, per ruling MR-07. Structural/support timber is 667.2 m³/yrTimberLabor_40!B5Live, ramp planking is 3,463.3 m³/yrTimberLabor_40!B6Live, and the total is 4,130.5 m³/yrTimberLabor_40!B7Derived — 82,609.5 m³TimberLabor_40!B27Derived over a 20-yearInputs_03!B81Source build.

Next move: Screen 4 converts the 82,609.5 m³ timber bill into the unit the historical record actually gives: ships.

Say which figure you are holding

The structural/support subtotal is 16% of the total. A reader who quotes 13,343.7 m³TimberSystem_31!B38Derived as the program's timber bill is quoting a sixth of it. That cell is correct for what it names — the twenty-year structural screen — and wrong for anything wider.

This page's timber total is always TimberLabor_40!B7 annually and B27 over the build.

And the barge fleet is left out of it

Hull timber for the granite barges runs to 80.6 m³/yrTimberLabor_40!B8Derived felled, and it sits outside the total above. The workbook says so in the cell note itself: excluding it is conservative (TimberLabor_40!E27).

It is native acacia built at riverside yards, so its sea voyage and its overland haul are also left out of the labor chain — again generous to the conventional account (TimberLabor_40!E8).

Screen 4 of 6

Count the ships, not the cubic meters.

Picture all the timber as cargo, including the wood supplied locally. At the assumed load per ship, it would fill about 1,204 shiploads over the build. Half of that timber is allowed to come from Egypt; the other half would require about 602 shiploads from abroad. Compare those numbers with the forty ships recorded on the Palermo Stone.

Baseline requirement — total throughput 1,203.8 Snefru-ship EQUIVALENTS of TOTAL timber throughput over the 20-year build, at the model's own Inputs_03!B202 68.625 m³/ship assumption. Not a claim that this much cedar was imported — ruling MR-10 separates the two, and the literal imported figures are below.
Palermo Stone: forty ships in one recorded delivery 40 ships recorded once in the Palermo cedar entry Inputs_03!B203Source
Additional gap — equivalents 1,163.8 additional ship equivalents beyond the record, on the total-throughput basis

Ruling MR-10 — two different questions, kept apart

The figures above measure the model's total timber throughput in units of one Snefru shipload. They are an equivalence, not an import claim. The literal imported-cedar requirement applies the 50% import lever (Inputs_03!B180) and is smaller: 2,065.2 m³/yrTimberLabor_40!B47 imported, which is 30.09 shiploads a yearTimberLabor_40!B48 — 0.75×TimberLabor_40!B49 the forty-ship record annually, below it. Over the build that is 601.9 shiploadsTimberLabor_40!B50, or 15.05×TimberLabor_40!B51 the record. The annual import figure sits below the record; the build-long figure is the one that carries this stream.

The record is fixed

40 shipsInputs_03!B203Source is the sourced quantity. It is the historical comparator, not the slider value and not a claimed import ceiling.

The slider is the assumption

68.625 m³/shipInputs_03!B202Assumption is the model's default cargo carried per ship. Moving right assumes larger or more capacious hulls, and the extra hull timber or capacity burden is not priced here. Change this and the required shipload count changes.

Break-even answers one question

103.26 m³/shipSensitivityBreakEven_06!B28Derived is not a new record. It is the cargo per ship the fixed forty-ship record would need in order to equal one year of timber demand. It is the threshold for the total-throughput annual-equivalence comparison, not the literal import rate: the complete timber system requires 4,130.5 m³ a year, equal to 60.19 Snefru-ship equivalents annually, while under the model's 50% imported-timber concession the literal seaborne requirement is 30.09 shiploads a year and 601.9 over the twenty-year build.

One year of shiploads against the forty-ship record One year of the program is drawn as a block of hull shapes, one shape per shipload, above a second block of forty shapes standing for the record. The program block is half as large again as the record block, and it grows as the reader lowers the cedar carried per ship. IN ONE YEAR Enough timber to fill about 60 shiploads each year THE RECORD — FORTY SHIPS, ONCE the largest single documented timber import of the period
The twenty-year consequence of the annual shipload requirement The whole-build figure is the annual shipload requirement multiplied by twenty years. The forty-ship record remains one documented delivery; it is not multiplied by twenty. OVER THE WHOLE BUILD 60.19 shiploads / year × 20 years 1,203.8 shiploads the forty-ship record remains one documenteddelivery, not a yearly allowance Moving the slider changes the assumed m³/ship, so both shipload counts recalculate.
68.625 m³ per ship
the model's value68.625 m³ break-even103.26 m³

Why this lever, and not another. Turning a timber bill into a number of voyages needs one figure the record does not give: how much cedar a ship carried. The Palermo entry counts ships. Nobody wrote down volumes. That single unknown is the denominator of every number on this screen, so it is the only thing here you can move.

Changing the assumed cargo per ship changes the number of shiploads required. Smaller cargoes require more voyages; larger cargoes require fewer. The recorded forty-ship delivery stays fixed. This control changes the cargo assumption, not the historical record or the rest of the transport system.

Includes both local and imported timber.

One year's timber, measured in shiploads 60.19 Shiploads needed to hold all the timber at this cargo size TimberLabor_40!B29Derived How many times the recorded forty-ship delivery? 1.50× TimberLabor_40!B32Derived
Twenty years of timber, measured in shiploads 1,203.8 Shiploads needed to hold all the timber at this cargo size TimberLabor_40!B30Derived How many times the recorded forty-ship delivery? 30.09×, of which 1,163.8 shiploads are beyond it B30 ÷ Inputs_03!B203, and TimberLabor_40!B33

The record itself never moves: forty ships is the sourced quantity, 40Inputs_03!B203Source (SourceRegister_01 SRC-PALERMO-CEDAR). The lever changes only what each hull is assumed to carry, so it changes how many voyages the program needs — not how many the record attests.

1,203.8 SHIPLOADS VS 40 SHIPS RECORDED ONCE At the model's own value, one year of the program needs 60.19 shiploads against a record of forty. Over twenty years that is 1,203.8 shiploads — 30.09× the largest single documented timber import.
103.26 m³ per ship Break-even, SensitivityBreakEven_06!B28Derived — what a single forty-ship delivery would have to carry per hull to cover one year of demand. The finding holds for any per-ship volume below 103.26 m³. The model assumes Inputs_03!B202 = 68.625 m³, already on the generous side. Argue the hulls larger and drag past the mark: the requirement is still there at every setting under it.
The per-ship volume is an assumption, and it is the denominator of every figure above Forty ships is sourced to Wilkinson's edition of the Palermo Stone, pp. 141–145. The volume each hull carried is not recorded anywhere. The workbook picks Inputs_03!B202Assumption = 68.625 m³ deliberately high, because a larger comparator shrinks the ratio and favors the conventional account. The slider is the honest treatment of that: the whole range is on the page, and the reader can put the number wherever they think it belongs. Ruling MR-06 settles which of the two is the sourced one. The record states a number of ships, so the count is held fixed at Inputs_03!B203Source and the comparator's total volume is derived from it as count × per-ship volume. Dragging the lever down therefore lowers the comparator and raises every ratio, which is the honest direction.
One documented steelman takes the annual figure below the record Doubling plank service life at Inputs_03!B192Assumption — the workbook's own steelman, mirrored at TimberLabor_40 rows 37–43 — halves the ramp stream and brings one year down to 34.96 shiploadsTimberLabor_40!B39Derived, or 0.87×TimberLabor_40!B40Derived the record. On that basis a single forty-ship delivery would cover a year, and the annual comparison above does not hold. What holds on every basis is the build: even steelmanned it takes 699.1 shiploadsTimberLabor_40!B42Derived over twenty years, 17.48×TimberLabor_40!B43Derived the largest delivery the record attests. The steelman is switched off in the figures above, and it is stated here rather than left for a reader to find.
Open, and badged unattested rather than disproven — SRC-CEDAR-PROCESSING-STATE The Palermo entry records ships of cedar wood and does not say what state the wood was in. This page counts the requirement as raw timber that must arrive, because the workbook places conversion loss after delivery (Inputs_03!B142). If the cedar arrived already squared or graded, that basis moves — and moving it is the stated reversal condition for ruling MR-07, which sets the felled basis this whole page rests on. SourceRegister_01 row 84 records the item as UNATTESTED at Low confidence: no source-side conversion installation is reported in the sources surveyed so far, and the primary reading task is open. One counter-datapoint is recorded rather than buried — Wenamun describes Byblos supplying timber shaped as stem-posts and keels, but that text is roughly 1,500 years later than Khufu.

Forty ships is a magnitude, never a ceiling

Nobody claims forty ships was the limit of what Egypt could import. Cedar moved from the Levantine coast for centuries, and the Palermo entry is one delivery that happened to be written down. It is here because it is the largest single documented timber import of the period — a sense of scale, not a cap (TimberLabor_40!E31).

The forty ships are a recorded delivery, not a limit on how many voyages Egypt could have made. But forty ships do not explain about 602 imported shiploads over the build, even with half the timber supplied locally. Where would that wood have come from? Who would have cut it, loaded it, sailed it to Egypt, and delivered it to the worksite, year after year?

Screen 5 of 6

The wood Egypt does have is already spoken for.

"They used local wood" is the first answer most readers reach for, and it is a fair one. The model does not wave it away. It gives native timber half the bill — 50%Inputs_03!B180Assumption imported, the balance native — and then runs the native half against the woodland the rest of the model is already drawing on.

The managed woodland divided among the things already drawing on it A single horizontal bar stands for the whole managed woodland of 2,169 square kilometres. It is divided by length into the draws already on it: a narrow slice for copper smelting, a very long section for bread and brewery ovens, and a narrow slice at the end for the timber this page counts, after the waste credit. Beyond the end of the bar sits a dashed empty box marked with a question mark: the fuel for firing mortar and gypsum, which the model does not quantify anywhere and which is therefore outside the total. WHAT IS ALREADY DRAWING ON THE SAME WOODLAND COPPER SMELTING 11,014.9 ha Model_04!B59 THE TIMBER THIS PAGE COUNTS the balance, after the waste credit is given back BREAD AND BREWERY OVENS 199,528.5 ha FoodSystem_13!B25 ? MORTAR AND GYPSUM FIRING — not quantified anywhere so it sits outside the total, and the total understates WoodFuelCredit_44!A30 2,169 km² OF MANAGED WOODLAND, ALL IN WoodFuelCredit_44!B24 Lengths along the bar are in proportion to area. 100 ha = 1 km². 2,169 km² is a square roughly 47 km on a side — about the width of Greater Cairo today. The two furnace draws are already in the model before any timber is cut.

Nothing here is exaggerated: the bar is one length, divided in proportion to area. The two furnace draws are the model's existing fuel-wood demand (Model_04!B59 and FoodSystem_13!B25, which together are the 2,105.4 km²FoodSystem_13!B27Derived of fuel woodland); the gold slice at the end is the balance up to 2,169 km²WoodFuelCredit_44!B24Derived, which is what every timber stream on this page adds once the waste credit has been given back. That balance is the difference between two cells printed here, not a cell of its own. The 47 km square and the comparison to the width of Greater Cairo are drawn, to give the area a size a reader can hold.

Even the local share has to come from this same woodland

Imported by sea Derived 2,065.2 m³/yr
The native balance Derived the rest of 4,130.5

The imported figure is 2,065.2 m³/yrTimberLabor_40!B13Derived, the total less that is the native balance, and the split is the 50%Inputs_03!B180Assumption lever. Bar lengths are in proportion. The local half is not free capacity: it has to be supplied by the same managed woodland already assigned to copper smelting, bread ovens, and brewery ovens.

Native stock does not settle the grade question. The imported share exists in the model because Egypt lacks structural softwood (Inputs_03!E180), and the chain on screen 1 already throws away 25%Inputs_03!B143Assumption of what is felled for species, dimension and defect before anything is installed.

Wood cannot be spent twice, and the model makes sure of it

Timber cutoffs, sawdust, rejects and spoiled stock are fuel, so the workbook credits 75%Inputs_03!B177Assumption of all timber waste against the fuel-wood bill — 1,357.2 t/yrWoodFuelCredit_44!B19Derived of credit, capped at actual fuel demand so it can never over-serve.

Burning every usable scrap covers 2.6%WoodFuelCredit_44!B21Derived of the fuel bill, leaving 51,278.6 t/yrWoodFuelCredit_44!B20Derived still to be cut. The credit closes the double-count objection. It does not close the woodland.

What the 2,169 km² does and does not include

Inside it: copper smelting fuel, bread and brewery oven fuel, and every felled timber stream including the barge fleet, with the waste credit already applied (WoodFuelCredit_44!B24).

Not inside it: the fuel for firing mortar and gypsum. The workbook names it as a competing draw on the same species and records plainly that it is not quantified anywhere in the model, so the 2,169 km² understates the requirement — "stated here rather than dropped", in its own words (WoodFuelCredit_44!A29, A30Policy). That omission runs in the conventional account's favor.

Screen 6 of 6

What this does and does not claim.

What is claimed

The model requires 4,130.5 cubic metersTimberLabor_40!B7Derived of felled timber each year, or 82,609.5TimberLabor_40!B27Derived over twenty years. That is enough wood to fill 60.19 shiploadsTimberLabor_40!B29Derived a year and 1,203.8TimberLabor_40!B30Derived over the build. With half supplied locally, imports would still total 30.09 shiploadsTimberLabor_40!B48Derived a year and 601.9TimberLabor_40!B50Derived over the build.

To fit one year's entire timber requirement onto forty ships, each would have had to carry 103.26 cubic metersSensitivityBreakEven_06!B28Derived. That calculation includes the local wood as well as the imports. It answers how much the ships would have had to carry, not how much ancient ships actually carried.

What is not claimed

  • Not that forty ships was Egypt's import capacity. It is the largest single import anyone wrote down. Cedar moved from the Levantine coast for centuries.
  • Not that the ramp recycling claim is false. It is true of the standing stock, which is under 170 m³. It has no bearing on the timber worn away, which is what the figures here count.
  • Not a labor or cost estimate for the fleet. The voyages are counted; harbor works, hull replacement and the Levantine end of the operation are unpriced here, not refused.
Open item 1 — the processing state of the cedar SRC-CEDAR-PROCESSING-STATE is OPEN and badged UNATTESTED, not disproven. The Palermo entry records ships of cedar wood and does not state processing state. If the cedar arrived already squared or graded, the felled basis moves — and that is the stated reversal condition for ruling MR-07, which sets the basis every figure on this page uses. SourceRegister_01 row 84, confidence Low.
Open item 2 — the volume each ship carried Per-ship volume is an Assumption at Inputs_03!B202, and it is the entire denominator of every shipload figure here. The ship count is sourced; the volume is not. The slider on screen 4 is the honest treatment: the reader sets it and watches the consequence.

Where the assumptions are generous, and which way that cuts

Barge hull timber is excluded from the rollup (TimberLabor_40!B8, E27), and so are the cedar voyage and overland haul for those hulls.

The plank service-life steelman is switched off (Inputs_03!B192 = 1, not the 2.0 the workbook offers). Turned on it halves the ramp stream, and it is the one lever that changes an answer here: a year falls to 0.87×TimberLabor_40!B40Derived the record, so the annual claim would not hold. The build-long claim would: 17.48×TimberLabor_40!B43Derived.

Per-ship volume is set high (Inputs_03!B202), so every shipload count on this page is the low end.

Mortar and gypsum firing fuel is left out of the woodland figure, because the workbook does not quantify it anywhere and says so (WoodFuelCredit_44!A30).

The felled basis is the one MR-07 rules for: the comparator counts raw cedar as it arrived, so the numerator counts raw timber as it must arrive. Log against log.

What this changes in the model

The IER ramp-timber material and wear screen remains a separately governed control finding (IERRampTimber_38!B40Policy). The labor is a different matter, and it is counted: TimberLabor_40 converts structural timber, ramp planking and barge-hull requirements into labor, and the resulting 1,709 rostered timber workers are integrated into M3 as Wave 3. Ramp labor is integrated as Wave 4. What stays outside the headline population total is the material screen on this page, not the people who cut, shape and install the timber.

What the finding means

The wood would not have arrived once and lasted twenty years. Worn planks would have needed replacing while construction continued. A construction explanation must show where all that timber would have come from and how it would have reached the worksite throughout the build, while the same people and resources were needed elsewhere.

Sources — every figure on this page, with its cell and its status

Read against QA_Integrated_Model_v0_92_USER_SOURCE.xlsx, SHA-256 4c719145…81580e. Statuses are the workbook's own: Source a pinned source, Assumption a chosen value, Derived computed from the others, Live a running total that moves as more work is costed, and Policy a recorded ruling.

The loss chain — screen 1

FigureValueCellStatus
Timber water damage / spoilage12%Inputs_03!B176Assumption
Handling / transport loss10%Inputs_03!B144Assumption
Structural reject / unsuitable25%Inputs_03!B143Assumption
Conversion / cut waste35%Inputs_03!B142Assumption
Combined usable yield38.61%WoodFuelCredit_44!B9Derived

The worked 100 m³ example, the 38.61 m³ result and the 2.59 factor are the register's own, at MethodsRulings_48 rows 9–19. The register states there that the example is illustrative at current lever settings and that all four rates are assumption levers; the ruling does not depend on their values, only on where in the chain they sit.

Ramp planking — screen 2

FigureValueCellStatus
Total blocks moved2,236,463IERRampTimber_38!B5Source
Loaded sledge-km on ramp surfaces670,264IERRampTimber_38!B6Source
Ramp lane width3.8 mIERRampTimber_38!B8Source
Planked share of running surface30%IERRampTimber_38!B17Assumption
Plank thickness0.07 mIERRampTimber_38!B18Assumption
Plank service life2,000 passesIERRampTimber_38!B19Assumption
Plank service-life multiplier (steelman)1 (steelman 2.0)Inputs_03!B192Assumption
Lane-meter replacement events over build335,132IERRampTimber_38!B24Derived
Timber per lane-meter replaced0.0798 m³IERRampTimber_38!B25Derived
Replacement planking installed over build26,743.5336 m³IERRampTimber_38!B26Derived
Standing stock, lanes at peak92.547 m³IERRampTimber_38!B28Derived
Standing stock, corner bays73.458 m³IERRampTimber_38!B29Derived
Planking felled including waste69,265.8213 m³IERRampTimber_38!B30Derived
Planking felled per year3,463.291 m³/yrIERRampTimber_38!B31Derived
Diagnostic is control-only, not added to the headlinePASSIERRampTimber_38!B40Policy
Timber demand needs labor-chain conversion firstOPENIERRampTimber_38!B41Policy

The 166.0 m³ standing figure printed on screen 2 is the sum of B28 and B29, both printed here. The workbook carries no single cell for the sum.

The timber bill and the delivery comparison — screens 3, 4 and 6

FigureValueCellStatus
Structural timber, harvested incl. losses667.1859 m³/yrTimberLabor_40!B5 ← TimberSystem_31!B37Live
Ramp planking replacement3,463.291 m³/yrTimberLabor_40!B6 ← IERRampTimber_38!B31Live
Total timber per year4,130.477 m³/yrTimberLabor_40!B7Derived
Barge hull timber, felled — outside the total80.6487 m³/yrTimberLabor_40!B8Derived
Imported volume2,065.238 m³/yrTimberLabor_40!B13Derived
Cumulative timber over build82,609.539 m³TimberLabor_40!B27Derived
Cedar per-ship volume (the lever)68.625 m³/shipTimberLabor_40!B28 ← Inputs_03!B202Assumption
Shiploads per year60.1891TimberLabor_40!B29Derived
Shiploads over the build1,203.782TimberLabor_40!B30Derived
Palermo / Snefru ship count — the record40 shipsInputs_03!B203 → TimberLabor_40!B31Source
Annual requirement as a multiple of the record1.504727×TimberLabor_40!B32Derived
Shiploads beyond the record, over the build1,163.782TimberLabor_40!B33Derived
Break-even cedar per-ship volume103.2619 m³/shipSensitivityBreakEven_06!B28Derived
Break-even annual shiploads40SensitivityBreakEven_06!B29Derived
Structural stream, cumulative — not the timber total13,343.718 m³TimberSystem_31!B38Derived
Palermo comparator volume (count × per-ship)2,745 m³Inputs_03!B146Derived
Build duration20 yrInputs_03!B81Source

The steelman mirror — plank service life at 2.0×

Added in v0.79 at TimberLabor_40 rows 35–43. The block mirrors the steelmanned result at the default setting so both can be read together; the workbook notes it is a pure sink and feeds nothing. Every figure elsewhere on this page is on the un-steelmanned basis.

FigureValueCellStatus
Ramp planking at 2.0× service life1,731.6455 m³/yrTimberLabor_40!B37Derived
Total timber per year, steelmanned2,398.8314 m³/yrTimberLabor_40!B38Derived
Shiploads per year, steelmanned34.9556TimberLabor_40!B39Derived
Annual multiple of the record, steelmanned0.873891×TimberLabor_40!B40Derived
Cumulative over build, steelmanned47,976.628 m³TimberLabor_40!B41Derived
Shiploads over the build, steelmanned699.113TimberLabor_40!B42Derived
Build-long multiple of the record, steelmanned17.477825×TimberLabor_40!B43Derived

TimberLabor_40!E39 records the consequence in the workbook's own words: the annual comparison does not survive the steelman, and the build-long one does. This page follows that instruction — it leads with the annual figure at the default setting and states the build-long figure wherever the steelman is raised.

The woodland ledger — screen 5

FigureValueCellStatus
Imported timber share50%Inputs_03!B180Assumption
Timber waste usable as fuel75%Inputs_03!B177Assumption
Fuel credit applied, capped at demand1,357.235 t/yrWoodFuelCredit_44!B19Derived
Net fuel wood still required51,278.612 t/yrWoodFuelCredit_44!B20Derived
Fuel demand met by timber waste2.5785%WoodFuelCredit_44!B21Derived
Total managed woodland2,169.056 km²WoodFuelCredit_44!B24Derived
Woodland for copper smelting11,014.889 haModel_04!B59Derived
Woodland for bread and brewery ovens199,528.500 haFoodSystem_13!B25Derived
Fuel woodland — smelting and ovens2,105.434 km²FoodSystem_13!B27Derived
Mortar and gypsum firing fuel — excluded, stated not droppednot quantifiedWoodFuelCredit_44!A29, A30Policy

Rulings this page follows

RulingWhat it settlesWhere
MR-07Timber ratios against the Palermo cedar comparator use the felled basis (IERRampTimber_38!B30), not the installed basis (B26). The denominator is raw cedar as it arrived, so the numerator must be raw timber as it must arrive. The installed basis returns 9.74× and is superseded; measuring the numerator at the installed end understates by a factor of 2.59. Ruled 2026-07-24, reaffirmed 2026-08-01. Reversal condition: evidence that the cedar arrived already converted, which is the open item SRC-CEDAR-PROCESSING-STATE.MethodsRulings_48 row 22
MR-06Which quantity in the Palermo comparator is the sourced one — the ship count or the volume? Ruled: the ship count. The record states a number of ships, not a number of cubic metres. The count is held at 40 (Inputs_03!B203, SOURCE), per-ship volume stays the assumption lever at B202, and the comparator's volume is derived as count × per-ship volume. Value-neutral at the default: 40 × 68.625 = 2,745. Ruled 2026-08-07. Reversal condition: the Palermo entry is shown to record a volume rather than a ship count.MethodsRulings_48 row 33
MR-01The model retains its 500 m mean ground-haul lever, because a fixed-point mean understates a distribution over an advancing quarry face. Recorded on the ramp sheet at IERRampTimber_38!A44.MethodsRulings_48 row 21

Open citations

SRC-CEDAR-PROCESSING-STATE — SourceRegister_01 row 84, confidence Low, status UNATTESTED. The Palermo Stone entry (Wilkinson, Royal Annals of Ancient Egypt, 2000, pp. 141–145) records ships of cedar wood without specifying processing state. No source-side conversion installation is reported in the sources surveyed to date and the primary reading task is open; survey targets recorded in the register are Mumford on Egypt in the eastern Mediterranean and Francis-Allouche & Grimal on the maritime approaches to Byblos. The register also records a reading caveat — Scalf on the seventh count of Snefru notes the initial column is difficult and has drawn various interpretations — and one counter-datapoint, Wenamun's New Kingdom account of Byblos supplying stem-posts and keels, roughly 1,500 years later. Unattested is not disproven, and the register says so.

SRC-PALERMO-CEDAR — SourceRegister_01 row 42, confidence Medium. The ship count of 40 is sourced to the cited pages. The per-ship volume of about 68.6 m³, and therefore the 2,745 m³ comparator total, is an assumption taken deliberately generous-high, because a larger comparator shrinks the demand ratio and favors the conventional scenario. Inputs_03!B146 carries its own note that the source and page trail is still to be hardened.

How the lever is bound, and what has no cell

The slider drives the workbook's own identities: B29 = B7 / B28 for shiploads a year, B30 = B27 / B28 over the build, and B32 = B29 / B31 against the record, with the record read from the sourced ship count at Inputs_03!B203 and held fixed wherever the lever is put. At the model's own value every readout equals its cell to the digit printed, and the cell reference is shown. Off that value the same identity is being applied to a per-ship volume the workbook does not carry, so the reference is withdrawn and the readout says so.

This was not true before v0.79. TimberLabor_40!B31 previously derived the record as Inputs_03!B146 / B28, which locked the record to the lever: lowering the per-ship volume raised the workbook's own "record" above forty, and B32 reduced algebraically to B7 / B146 — invariant to the lever, so a slider bound to it would have moved nothing. Ruling MR-06 fixed it by making the ship count the sourced quantity and deriving the comparator volume from it. The values at the default are unchanged.

One value-neutral inconsistency remains, stated rather than smoothed over: SensitivityBreakEven_06!B28 still divides by a literal 40 rather than reading Inputs_03!B203. It returns the same 103.2619 m³/ship and nothing on this page changes, but the literal will not follow the cell if the count is ever re-sourced.

Four figures printed here are arithmetic between other figures on this page rather than cells of their own, and are labeled as such where they appear: the 166.0 m³ standing stock (B28 + B29); the 30.09× build-long multiple of the record (TimberLabor_40!B30 ÷ Inputs_03!B203); the woodland balance the timber streams add (WoodFuelCredit_44!B24 − FoodSystem_13!B27); and the native timber balance shown as "the rest of 4,130.5".

The build-long multiple is worth naming as a gap rather than a quirk. The workbook carries an annual multiple of the record at TimberLabor_40!B32 and a build-long one under the steelman at B43, but none at the default setting — so the single figure that most directly answers "how much bigger than the record is the whole program?" has to be computed on the page. It would sit naturally as a new cell beside B33.

Illustrative geometry — every dimension that is drawn, not from the workbook

These values are prototype-only. They exist so the quantities can be seen against one another. They are not historical evidence, they are not from the workbook, and no conclusion on this page rests on them. They live in one object, illustrativeGeometry, in this page's script.

Drawn dimensionValueWhat it is for
Screen 1 — segment widthsequal, 150–180 pxPresentational only. Height alone carries the volume, at 2 px per m³. The four loss rates multiply, so their display order carries no meaning either.
Screen 2 — lane length drawn14 mA sample length of lane, so the 3.8 m width and the 30% planked share can be seen. The workbook supplies areas and volumes, not a length of lane.
Screen 2 — plank thickness exaggeration10× in the section only0.07 m at the lane's own scale is under two pixels. Only the section is stretched; the plan is unstretched.
Screen 2 — stock-versus-throughput ledger400 px = 69,265.8 m³The two right-hand volume bars use one line scale. The 166.0 m³ standing stock is shown separately as a small marker, because it is an at-one-moment stock rather than the build-long flow.
Screen 2 — replacement-event guidefour guide linesThe guide lines are presentational only; they show accumulation from many lane-meter replacement events, not a second quantitative scale.
Screen 3 — one scale throughout240 px = 4,130.5 m³Every one of the twenty columns is drawn identically, and the barge sliver uses the same scale. Nothing on the screen is compressed to fit.
Screen 4 — hull glyph20 × 7 px trapezoidA counting token, not a vessel. It carries no dimensions and makes no claim about hull form. Both blocks in the left panel use the identical glyph so the counts compare directly.
Screen 4 — glyphs per row20Layout only.
Screen 4 — year bars, right panel20 bars, equal lengthThe build is not drawn as 1,204 countable shapes, which no eye can read. It is drawn as twenty equal years, and the record is drawn against one of them as the fraction of a single year forty ships represents.
Screen 4 — slider range30 to 140 m³ per shipRuns well past the 103.26 m³ break-even on purpose, so the reader can argue the hulls larger and watch the requirement persist below it.
Screen 5 — bar length860 px = 2,169 km²One bar, divided in proportion to area. No exaggeration anywhere in the figure.
Screen 5 — the 47 km square√2,169 km² ≈ 47 kmA size the reader can hold, and the comparison to the width of Greater Cairo with it. Neither is in the workbook, and the model does not place the woodland anywhere on the map.
All diagramsno perspective, no rasterFlat shapes, dimensions, leaders and labels. Meaning is carried by position, fill and length; nothing is keyed by hatching.