rafatahmed · Oct 19, 2026 · Oct 19, 2026 · Oct 19, 2026 · Oct 19, 2026 · Oct 19, 2026
diff --git a/CHANGELOG.md b/CHANGELOG.md
@@ -4,6 +4,7 @@
 
 - Add experimental irrigation EC25 from speciation (McCleskey 2012 Eq. 8) with explicit partial results, envelope checks and provenance; no accuracy claim.
 - Irrigation EC (M2a): species without a McCleskey coefficient now give a bounded `estimated` result (`bounded`, `ec25_range_ms_cm`, midpoint `ec25_ms_cm`, `uncertainty_ms_cm`, audit `uncovered_bound_ms_cm`; upper limit from 80 S cm2/mol per charge) instead of `partial`; `MODEL_VERSION` is now m2a and `compare_measured_ec` reports `ec25_range_ms_cm` and `within_range`.
+- Irrigation EC (M2b): H2PO4- and HPO4-2 now contribute through 25 C coefficients fitted to Pethybridge, Talbot and House (2006) Table III (`tools/fit_phosphate_conductivity.py`, `supplementary` block of the coefficient file, data to I = 0.014); the audit records `supplementaryCoefficients` and `phosphate_fit_max_ionic_strength`, and `MODEL_VERSION` is now m2b. Minor phosphate pairs and PO4-3 stay under the bound.
 - Add the material traceability API (`docs/materials.md`): shipped identity records (`load_identities`, `identity_for_product`), user grades and lots (`make_grade`, `make_lot`), `resolve_material` (per-nutrient basis, band ends, flags, provenance) and `nutrient_band`; `catalogue_dose_totals` and `calculate_irrigation_ec` take `materials=`, undisclosed blends raise or report `composition_undisclosed` in chemistry, and EC and equilibrium-delivery audits carry material provenance.
 - Link every catalogue product in `library.json` to its chemical identity (`identityId`) and record its `analysisBasis` (`declared_catalogue`, `identity_theoretical` or `grade_typical`) and `source` document reference. Product `id` and `name` values are unchanged.
 - Correct Mg Nitrate to Mg(NO3)2·6H2O theory (owner decision D1): formula `Mg(NO3)2` → `Mg(NO3)2.6H2O`; N_NO3 11 → 10.92564 %, Mg 9.65 → 9.47931 %; basis `identity_theoretical`. Its declared-form charge residual at 1 g/kg water goes from +0.5532 % to ~0 %, so it no longer trips the EC O5 gate on its own.

diff --git a/docs/conductivity.md b/docs/conductivity.md
@@ -125,10 +125,10 @@ still be reported when EC evidence is missing; that does not approve the recipe
 or authorize EC-driven correction. Verify EC after preparation/dilution using
 meters rated for the relevant stock and irrigation ranges.
 
-## Calculated irrigation EC (experimental, M2a)
+## Calculated irrigation EC (experimental, M2b)
 
 Purpose: estimate the EC of an irrigation solution before mixing, and compare
-it with a meter reading after mixing. This is **experimental (M2a)** and Python
+it with a meter reading after mixing. This is **experimental (M2b)** and Python
 only: there is no CLI flag and no grower-facing number. It is separate from the
 calibration-based planner above.
 
@@ -141,7 +141,7 @@ applied.
 
 | Status | Meaning |
 |---|---|
-| `estimated` | Every charged species above 1e-12 mol/kgw has a McCleskey coefficient, or the species without one are covered by the bound below. `ec25_ms_cm` is the estimate. |
+| `estimated` | Every charged species above 1e-12 mol/kgw has a McCleskey coefficient, or the species without one are covered by the bound below, or a supplementary 25 C coefficient (H2PO4-, HPO4-2). `ec25_ms_cm` is the estimate. |
 | `partial` | With a `supplied` pH, there are unrecorded counterions (`unrecorded_counterions`, rule O5) reported in eq/kgw. Only a known-species subtotal is reported, with no total. |
 | `not_supported` | Outside the envelope (temperature, ionic strength, non-closed carbon) or the assay charge residual is too large. `reason` says which; no EC is reported. |
 
@@ -154,7 +154,7 @@ it is over the speciated absolute equivalents. Above it, a `supplied` pH gives
 `not_supported` (`assay_charge_residual_too_large`).
 
 Bounded estimates (decision O2): charged species with no McCleskey coefficient
-(H2PO4-, MgOH+, CaOH+, charged chelates) no longer make the result `partial`.
+(KHPO4-, CaH2PO4+, MgOH+, CaOH+, charged chelates) no longer make the result `partial`.
 Their contribution is non-negative, so the known subtotal is a lower limit. The
 upper limit adds sum(|z| x 80 x m) over those species, because no ion's limiting
 molar conductivity exceeds 80 S cm2/mol per unit charge at infinite dilution
@@ -164,18 +164,26 @@ molar conductivity exceeds 80 S cm2/mol per unit charge at infinite dilution
 - `ec25_range_ms_cm`: `(known subtotal, known subtotal + bound)`; the range extends only upward from the known subtotal, because missing contributions cannot be negative.
 - `ec25_ms_cm`: the midpoint; `uncertainty_ms_cm`: half the bound.
 - `audit["uncovered_bound_ms_cm"]`: the bound; `missing_species` still lists every uncovered species.
-- `transport_numbers` is `{}`, and `MODEL_VERSION` is `irrigation-ec-mccleskey2012-m2a-experimental`.
+- `transport_numbers` is `{}` for bounded results, and `MODEL_VERSION` is `irrigation-ec-mccleskey2012-m2b-experimental`.
 
 The midpoint and `uncertainty_ms_cm` describe only the uncovered-species interval; they are not an accuracy statement and exclude model error. Because 80 S·cm²/mol per charge is conservative, the true value tends to lie in the lower half of the range.
 
 `partial` arises only from unrecorded counterions; temperature, carbon,
-ionic-strength domain and undisclosed blends give `not_supported`. All 26 shipped formulas return `estimated`, with ranges up to 14.4 % of
-the midpoint (Generic Wet Season). Phosphate coefficients are not yet
-measured, so phosphate stays under the bound until M2b. `compare_measured_ec`
+ionic-strength domain and undisclosed blends give `not_supported`. All 26 shipped formulas return `estimated`, with ranges up to 5.4 % of
+the midpoint (Generic Wet Season, mostly citrate pairs; 14.4 % before the
+phosphate coefficients).
+
+**Phosphate (M2b).** H2PO4- and HPO4-2 are covered at 25 C by coefficients
+fitted to the measured KH2PO4 and K2HPO4 conductivities of Pethybridge,
+Talbot and House (2006), Table III, through FlahaX speciation (lambda0 and A
+fitted, B = 1.5; RMS 0.13 % over 22 points). The data reach I = 0.014 mol/kgw;
+above that the fit is extrapolated, and the audit records
+`phosphate_fit_max_ionic_strength` and `supplementaryCoefficients`. PO4-3 and
+minor phosphate pairs such as KHPO4- stay under the bound. KHPO4- is not covered; the fitted HPO4-2 coefficients absorb part of its current, so the upper end of a mixture's range may count it twice (small and conservative). `compare_measured_ec`
 also returns `ec25_range_ms_cm` and `within_range` (True, False, or None when the
-prediction is not bounded); it is a fact, not a pass/fail verdict.
+prediction is not bounded); it is a fact, not a pass/fail verdict. `within_range` does not include model or meter error, so when the range is narrow a False value says nothing about agreement.
 
-Example (KH2PO4 at 1 g/kg water, calculated pH):
+Example (KH2PO4 at 1 g/kg water, calculated pH). With the phosphate coefficients the remaining bound is below 0.001 mS/cm, so a 0.80 reading lies outside the range:
 
 ```python
 from flahax import calculate_ec_from_totals, compare_measured_ec
@@ -197,10 +205,10 @@ Output:
 
 ```text
 estimated True
-[0.524, 1.113]
-0.818 0.295
-['H2PO4-', 'HPO4-2', 'KHPO4-', 'PO4-3']
-True
+[0.738, 0.738]
+0.738 0.0
+['KHPO4-', 'PO4-3']
+False
 ```
 
 ```python
diff --git a/docs/development-status.md b/docs/development-status.md
@@ -14,7 +14,7 @@ The matrix below describes the 0.3.1 capabilities and their boundaries.
 | Industrial acid selection and product mass/volume | Standard workflow HNO3/H3PO4, `acid_selection.py`, four preserved lower-level PHREEQC acid fixtures | Supplied assay/density/provenance, nutrient and volume limits; no automatic dosing approval |
 | Source-specific CLI | `planning_cli.py`, `__main__.py`, `test_site_planning.py` | Explicit JSON/interactive inputs, no default water or equipment model |
 | No-new-measurements EC screening | `calculated_ec.py`, exact SQM anchors with source hash, regression tests | Pre-acid dilute approximation at 25 C, restricted loading, unknown accuracy; incomplete products yield no total |
-| Calculated irrigation EC (McCleskey 2012 on speciation) | `irrigation_ec.py`, transcription and rule tests | Experimental M2a; phosphate and chelate species give a bounded range; no measured accuracy |
+| Calculated irrigation EC (McCleskey 2012 on speciation) | `irrigation_ec.py`, transcription and rule tests | Experimental M2b; H2PO4-/HPO4-2 fitted to Pethybridge 2006 Table III; minor pairs and chelate species give a bounded range; no measured accuracy |
 | Optional measured-profile EC method | `conductivity.py`, synthetic regression profiles | Requires matching measured evidence when used; example profiles are fictional |
 | A/B and acid report clarity | `pepper_stock_review.py`, HTML/Markdown/JSON examples and tests | Candidate grouping only; trace locations unresolved; no approved full pepper StockPlan |
 | Stock planning API | Existing sourced compatibility/solubility/capacity checks | Caller must supply complete applicable records; absence from a pairwise table is not evidence of compatibility |

diff --git a/docs/superpowers/plans/2026-10-19-irrigation-ec-m2.md b/docs/superpowers/plans/2026-10-19-irrigation-ec-m2.md
@@ -70,25 +70,30 @@
   - `test_band_ends_carry_own_bounds` (Review Focus 4): a graded KH₂PO₄-like case where the ends differ.
 - [ ] **Implement, run, full suite, then commit** with the message "Report range membership for bounded EC estimates".
 
-### Task 3 (M2b): Phosphate coefficients from measured data. BLOCKED until the owner supplies data.
+### Task 3 (M2b): Phosphate coefficients from Pethybridge et al. 2006 (amended O1)
 
-**Precondition (controller checks; if missing, stop and report BLOCKED):**
-- `tests/fixtures/conductivity/crc_phosphate_lambda0.json`: owner-checked CRC λ° for H2PO4-, HPO4-2 and PO4-3, with the edition and page.
-- `tests/fixtures/conductivity/muccitelli1994_25c.json` and an independently typed copy `..._independent.json`. They hold every 25 °C KH₂PO₄ and K₂HPO₄ point (concentration in mol/L, κ in µS/cm or as printed, with units) from Muccitelli & DiAngelo (1994), plus the paper's DOI and the PDF SHA-256.
+**Inputs:**
+- `tests/fixtures/conductivity/pethybridge2006_table3.json` is the owner's first transcription. The controller writes it from the owner's message, with the citation, doi, units and the ½K₂HPO₄ heading convention.
+- `..._independent.json` is typed by a separate agent from the PDF in `docs/sources/` (step 3b). **Merge gate:** both copies must agree.
 
 **Files:**
-- Create: `tools/fit_phosphate_conductivity.py` (reads the fixtures, converts mol/L to mol/kgw with a stated density of water at 25 °C, speciates with FlahaX, and fits A and B per phosphate ion by least squares on κ with λ° fixed).
-- Modify: `src/flahax/data/conductivity_mccleskey2012.json`. Add a top-level `"supplementary"` section with `{ion: {lambda0_25c, A_25c, B, source, fit_rms_percent, points}}`. Do not add these ions to the McCleskey `ions` table, because they are not in the paper.
-- Modify: `irrigation_ec.ionic_molal_conductivity` / `covered_species`, so supplementary ions are covered at 25 °C only.
-- Test: `tests/test_irrigation_ec.py` (class `PhosphateCoefficientTests`).
-
-- [ ] **Failing tests:**
-  - `test_fixture_transcriptions_agree`;
-  - `test_fit_reproduces_measurements` (each point within the published RMS, which is ≤ 2 %);
-  - `test_phreeqc_cross_check` (CRC λ° within 15 % of the `phreeqc.dat`-derived 31.8 / 103.6 / 206.8; report, don't hide);
-  - `test_kh2po4_now_covered`: KH₂PO₄ totals give an unbounded `estimated` result, or a much smaller bound if minor pairs remain.
-- [ ] **Run the tool**, commit its output, then run the full suite. Recount the 26 formulas and record the narrowed ranges in the design §13.
-- [ ] **Commit** with the message "Add phosphate conductivity coefficients fitted to measured data".
+- Create `tools/fit_phosphate_conductivity.py`.
+  - **Inputs:** the fixture. Concentrations in mmol/dm³ convert to mol/kgw using a water density of 0.997047 kg/dm³ at 25 °C, a recorded constant.
+  - **Conductivity:** κ (mS/cm) = Λ × c(mmol/dm³) / 1000. The K₂HPO₄ rows use ½-formula units, so salt molarity = c/2.
+  - **Speciation:** each point uses `calculate_equilibrium_ph({'K+': n·m, 'PO4-3': m}, complete_analysis=True, carbon_boundary='closed', phases=[])`.
+  - **Fit:** weighted linear least squares (weight 1/κ²) for λ° and A of H2PO4- and HPO4-2, with B = 1.5 fixed.
+  - **Output:** the supplementary block, JSON on stdout, written with `--write`.
+- Modify `src/flahax/data/conductivity_mccleskey2012.json`. Add a top-level `"supplementary"` block: `{"H2PO4-": {"lambda0_25c", "A_25c", "B": 1.5}, "HPO4-2": {...}, "source": {citation, doi, table: "III"}, "fit": {rms_percent, points, max_ionic_strength, density_kg_dm3}, "cross_checks": {...}}`. The McCleskey `ions` table stays untouched. Update `COEFFICIENTS_SHA256` / the literal pin test.
+- Modify `irrigation_ec.py`. `ionic_molal_conductivity` and `covered_species` include the supplementary ions (25 °C only; any other temperature raises). The audit gains `phosphate_fit_max_ionic_strength` and `supplementaryCoefficients: true` whenever a supplementary ion contributes. Bump `MODEL_VERSION` to `irrigation-ec-mccleskey2012-m2b-experimental`.
+
+- [ ] **3a. Failing tests** (class `PhosphateCoefficientTests`):
+  - `test_fit_reproduces_table3`: running the tool on the fixture reproduces the shipped supplementary block to 1e-9, and every point is within 0.5 %.
+  - `test_cross_checks_reported`: fitted λ° vs CRC (36, 114), Pethybridge (33.33, 115.14) and phreeqc.dat (31.8, 103.6). Report the percent gaps and assert ≤ 15 %, or document a larger gap in the block.
+  - `test_kh2po4_now_mostly_covered`: KH₂PO₄ totals (1/136.09 mol/kgw) are bounded only by minor pairs, and the range width is below 5 % of the midpoint (it was ±36 % under M2a).
+  - `test_supplementary_not_in_mcCleskey_table`.
+  - `test_all_shipped_formulas_estimated`: tighten the width ceiling to the new observed maximum plus margin, and record the numbers.
+- [ ] **3a. Implement, run the tool, commit its output, run the full suite** (in the background, waiting for it). Recount the 26 formulas into design §13. Commit with the message "Add phosphate conductivity coefficients fitted to Pethybridge et al. 2006".
+- [ ] **3b (needs the PDF):** a separate agent types `pethybridge2006_table3_independent.json` from the PDF. Add `test_table3_transcriptions_agree`. If any value disagrees, stop and report to the owner. Commit with the message "Check Pethybridge Table III against an independent transcription".
 
 ### Task 4: Docs, exports, verification