Retrospective IRAC colour evidence for the three positional cases

Retrospective IRAC colour evidence for the three positional cases

12 October 2026. This is a distinct, bounded physical-evidence diagnostic under RESEARCH_GOAL.md, not another run of the failed native association or ranking comparison. It asks whether the retained counterpart photometry supplies the necessary red colours of one established IRAC Class-I selection scheme. A stable position and a chemistry rank are not youth evidence. This check addresses that specific interpretation gap before any further fitting or observations.

Consumption and exact scope

The three cases and the best positional Catalog records are already selected, consumed and read. Their magnitudes were inspected before this diagnostic was registered and appear near zero colour. The selection is not representative, untouched validation or a preregistered physical discovery. Freeze this diagnostic implementation, exact inputs, literature contract and reporting rules in Git before execution. No new photometry, source choice, flag exemption or old rule is permitted. Keep all six Catalog records and six Archive aliases as alternatives, not twelve independent objects. Best records remain those in the verified cards:

Retain exact IDs, native magnitudes/errors/fluxes and missing values, the original rank scores, flags, membership/stage unknowns and all earlier failed gates. The 19,328-clump parent and its 19,066 unknown proxy states stay unchanged. Results concern these counterpart records, never every emitter inside their dust clumps.

Published comparator and applicability

Gutermuth et al. (2009), Appendix A.1, pp.27–29 (PDF pages indexed 26–28), arXiv:0906.0201v1, DOI 10.1088/0067-0049/184/1/18, specifies four IRAC detections with magnitude uncertainties <0.2 mag and contaminant rejection before Class-I colour selection. The two colour conditions are [3.6]-[4.5] >0.7 mag and [4.5]-[5.8] >0.7 mag. These are a necessary colour component of that scheme, not a universal definition of a physical protostar. Other phases require additional near-IR or 24-micron evidence.

Implement only this declared applicability/necessary-colour component, not the full contaminant or Class-I/II classifier. Missing near-IR/24-micron evidence means those alternative routes are not evaluated; identifiers are not photometry. Missing 8-micron photometry is not an upper limit or physical nondetection. Missing per-band quality flags, extinction, deblending and ownership also remain unresolved. Do not call this a complete standard-consensus classification.

Frozen calculation and sensitivity

Use native Vega magnitudes directly. A band is calculable only if magnitude and positive quoted magnitude error are finite, and native flux and error are finite and positive. Preserve blank strings and invalid reasons; never impute a missing band as zero, derive a flux limit from absence or pool Catalog/Archive aliases. Compute all six band-pair colours for every retained record, especially c12 and c23. Four-band photometric availability requires four valid bands, each quoted magnitude error <0.2. This is necessary availability, not full quality eligibility.

For colour c=m_a-m_b and unknown correlation rho in [-1,1], linear quoted-error propagation gives Var(c)=s_a^2+s_b^2-2rhos_as_b. Its standard deviation range is [|s_a-s_b|,s_a+s_b]. Record the independent-error reference sqrt(s_a^2+s_b^2) but do not assume it is validated. Compute c +/- k(s_a+s_b) for fixed k=1 and 3. These are quoted-error sensitivity envelopes, not calibrated confidence bounds, physical exclusion regions, upper limits or posterior probabilities. Corrected photometry, unmodelled systematics and non-Gaussian error may lie outside them. Shared bands induce joint colour covariance; do not multiply marginal probabilities or infer a joint compatible solution just because two marginal envelopes overlap.

For each of the three fixed best records, record:

  1. four-band photometric availability and exact missing/invalid bands;
  2. central c12/c23 >0.7 necessary condition, or unknown when missing;
  3. robust necessary-colour support if both lower 3x envelopes exceed 0.7;
  4. quoted-error incompatibility if at least one available upper 3x envelope is <=0.7; otherwise unresolved, never classify the source as starless/field star;
  5. 1x and independent-error-reference values as explicitly secondary diagnostics.

The endpoint is a three-row decision table and counts for those fixed states. The red-colour support criterion is both robust inequalities, not a post-read new astrophysical threshold. Missing/inapplicable full classification remains unknown even when a necessary central colour fails. No primary ranking gain, physical precision, population recall, birth, membership or occurrence is measured.

Reproducibility, controls and stopping

Hash-bind the six complete original responses, native-source CSV, verified cards, association summary and independent receipt, final native checkpoint, literature contract and new protocol/code. Verify each card’s chosen native source against response key and exact ordinal/counter and retain every alternative. Generator uses decimal differences/envelopes with floating square-root reporting; the independent verifier reads raw responses directly, uses exact Fraction arithmetic, derives all pair values independently and verifies card/native links, all outputs and endpoint counts without importing the worker. Synthetic checks cover missing bands, strict > boundaries, equality, unknown covariance extremes, invalid errors and shared-band covariance.

Offline only, one CPU, no GPU, no network worker or model rerun. Guard each worker at 256 MiB sampled RSS, ten minutes and 1 MiB of outputs including resource receipts. Combined report/registration/analysis/verification/code <=4 MiB; maintain 5 GiB free. Stop on hash, schema, identity or resource failure; retain failed attempts. Do not automatically substitute sources, acquire bands or retune cuts. Finish with a source-bound positive, incompatible or insufficient colour-evidence assessment and its physical limitations; verify independently and snapshot in Git. The full detector goal remains unmet. A further unit needs distinct justification.