Herodotus' multiplicative fog

Resolution criteria: POPULATION: every explicit numeric distance in the Histories (books 1-9) between two geographically identifiable termini - point-to-point, route, or sea-crossing distances. EXCLUDED: building/wall dimensions and city circuits; vague non-numeric distances; termini with no mainstream geographic identification (excluded rows recorded with reasons). Duplicate statements of the same pair+figure collapse to one row (first locus primary). UNITS, per Herodotus' own stated equivalences, fixed conversion table recorded per row: stade = 185 m; parasang = 30 stades (5.53); schoinos = 60 stades (2.6); land day's journey = 200 stades (4.101); day's sail = 700 stades, night's sail = 600 stades (4.86). The stade-length choice shifts only the location of log-errors, not their variance, shape, or the model comparison, so the primary clause is insensitive to it; a 157.5 m sensitivity is narrative only. TRUE VALUES: WGS84 geodesic between Pleiades coordinates for direct and sea segments; documented path-following approximation for distances the text explicitly gives along a named route (Royal Road stages, Nile voyage); method recorded per row. Contested identifications: mainstream identification used, row flagged identification_confidence=low and EXCLUDED from the primary analysis (sensitivity including them is narrative). HOP BANDS, fixed here at registration and applied mechanically by the builder from the remoter terminus of each pair (documented informant chains are recorded per row as narrative but the band table governs): Band 0 (autopsy-plausible core) = mainland Greece, the Aegean, western Anatolian coast, Lower Egypt up to Elephantine; Band 1 (direct Greek contact) = the rest of Anatolia, Levant coast, Cyrenaica, Black Sea coasts, Magna Graecia and Sicily, coastal Thrace and Macedon; Band 2 (one remove) = Persian interior and Mesopotamia, Scythian interior, the Nile above Elephantine to Meroe, inland Thrace and Illyria, the Libyan oases chain; Band 3 (deep hearsay) = India and beyond, the Caspian and beyond, the Nile beyond Meroe, peoples beyond the Scythians (Argippaei, Issedones and further), the circumnavigation of Africa, the far west and north of Europe. STATISTICS, computed only by the shepherd after corpus freeze: log_error = ln(reported/true). A band is populated iff n >= 8 primary rows. Multiplicative model: reported ~ LogNormal(ln(true) + mu_band, sigma_band^2); additive model: reported ~ Normal(true + a_band, s_band^2); both fit by MLE with per-band parameters, AIC compared on identical row sets. CLAUSE PRECEDENCE, evaluated strictly in this order, applicable only when >= 3 bands are populated (fewer than 3 populated bands is never a kill - it falls to clause 3): (1) KILLED iff, taking all populated bands in index order, their sample variances of log-errors are NOT strictly increasing (any later populated band with variance <= an earlier one), OR the additive model has the lower AIC. (2) SUPPORTED iff there are >= 3 populated bands, their sample variances are strictly increasing across ALL populated bands in index order, Shapiro-Wilk on log-errors within EVERY populated band gives p > 0.05, AND the multiplicative model has the lower AIC. (3) Otherwise INCONCLUSIVE - explicitly including: fewer than 3 populated bands; variance strictly increasing and multiplicative winning but any within-band Shapiro-Wilk p <= 0.05. Narrative (non-binding): permutation p-value for the variance ordering, per-band medians, sensitivity with low-confidence rows and alternate stade length.

Known priors disclosure: Seen at registration: the shepherd triage (adjacent) located systematic reported-vs-true discrepancy estimation in the itinerary-stadion literature (Eratosthenes/Strabo tradition) and the well-studied autopsy-vs-hearsay source hierarchy in Herodotean Quellenforschung; the specific model - log-error variance growing with informant-hop count in Herodotus - was not located. Noetic priors honestly held: expectation that Egyptian and Anatolian figures are comparatively accurate and Scythian/far-eastern figures inflated; Herodotus' own unit equivalences (2.6, 4.86, 4.101, 5.53) known, including his awareness that the schoinos varies. No error statistic of any kind has been computed: the corpus does not exist, no distance rows have been extracted, and the build agent has not been launched at registration time.

Exactly the registered criteria (packet e5c4a79e, ModelRun 26009): log_error = ln(reported_m/true_m) per primary row; band populated iff n >= 8; clause precedence applicable only when >= 3 bands are populated, else clause 3. Computation script committed at docs/generated/instrument_builds/herodotus-distances/shepherd_analysis.py (host python + scipy 1.18.0); narrative diagnostics (variance ordering, Shapiro-Wilk, per-band-parameter AIC comparison, low-confidence sensitivity) computed as registered non-binding.

Dataset: The B1 Herodotus Reported-vs-True Distance Corpus, built THIS DAY by the lane itself from the 'Not yet built' registry exhibit (inst-unbuilt-herodotus-distance-corpus): a census of explicit numeric distances in the Histories from Macaulay's PD text with Pleiades CC-BY geocoding - 110 candidate rows, 54 population-qualifying, 35 included_primary after the registered identification-confidence exclusion (19 low-confidence rows excluded from primary), frozen at sha256 4529bcee/commit d1d4be8 with the builder banned from computing any error aggregate.

computed 2026-07-16