# T618 build handoff

Built the private draft **Mass-radius constants of Lane–Emden polytropes**:
https://numberdb.org/T618 . It contains nine 100-significant-digit values at
n=1/2,1,3/2,2,5/2,3,7/2,4,9/2. No offer, review or publication action was made.
The controller must obtain the separate critique, its independent numerical
checks and fingerprint-bound argument-selection sidecar before offering it.

## Meaning and selection

The coefficient is N_n in K=N_n G M^((n-1)/n) R^((3-n)/n), for
P=K rho^(1+1/n), not a radius coefficient in a different normalization.
Princeton equations (poly.11a,b), Pols equation (4.15), and Lu equation (5)
agree on this convention. The family notation xi_1 and mu_n replaces Pols's
z_n and Theta_n. The table follows issue #246 and links the five existing
companions T613–T617 using slugs read from their actual pages.

The sole parameter n has domain 0<n<5 and a mixed selection: intrinsic {1},
documented_application {3/2,3}, and reference_sample
{1/2,2,5/2,7/2,4,9/2}. argument-selection.md gives the reference_policy,
noncanonical bounds, breadth rationale, exclusions and checked sources.
The incompressible index zero cannot be substituted into this EOS coefficient;
five has no finite radius. Index three is regular here and remains included.
No mathematical convention was left unresolved. The numerical method is
explicitly heuristic (agreement-checked), not a certified ODE enclosure.

## Checks and evidence

* Recomputed every background at 150 and 210 working decimal digits, varying
  order (160/210), step cap (1/12 versus 1/18), and central matching radius
  (1/2 versus 2/3). Worst relative coefficient difference:
  1.816401078546671e-154. Retained only 100 significant digits.
* The exact index-one coefficient 2/pi uses Arb balls. Numerical integration
  also reproduces this anchor; no known rational values are stored as decimals.
* An independent radial-coordinate integration with exact rational central
  coefficients and a pressure integral recovers the mass from the virial
  identity before reconstructing N_n. The index-zero and index-one backgrounds
  are positive controls, and displaced controls are rejected. All nine
  coefficient checks meet the required relative tolerance 1e-40; the worst
  measured coefficient discrepancy is 1.7686873200833423e-73. This is build
  validation, not the campaign's independent critique.
* All six overlaps agree with the last-place precision of Pols, Table 4.1.
* The maintained dry_run.py passed exactness, exact-in-disguise, prose and size
  checks: nine entries, longest internal representation 158 characters, 1.8 KB.
  The actual stored decimal values are at most 102 characters long.
* Generator verify() matched all nine stored entries. readback_checks.py tests
  their actual last-place intervals, the analytic anchor, radius/mass and
  pressure/concentration relations, and physical scaling at two independent
  choices of scale and central density. Readback evidence accompanies this report.
* The authenticated site audit reports clean=true and no findings. Public API
  readback confirms the table remains private. No outward-link-check option
  exists on this audit endpoint; mathematical sources were separately fetched,
  and every companion slug was read from the corresponding live table page.

Reproducible sources and evidence are attached to the draft. The primary
solver.py is the unmodified source downloaded from T617. source-manifest.json
records the source URLs and hashes. compute.log, independent.log, fill-check.log
and readback-final.log retain the run output locally. The failed readback.log is also preserved. The initial interval checker
had a Sage RealField-versus-RealIntervalField threshold comparison error;
an absolute-width assumption also needed replacement by a relative-width check for the 100-significant-digit companion values. Only the checker was corrected, with no change to any stored number. lesson-proposal.md records the portable checking lesson.
The website's empty-document replacement refusal and safe workaround are
recorded in environment-findings.md.

Versions: SageMath 10.9, numberdb 0.1.10, mpmath 1.4.1, Python 3.12.3.

## Skill alignment and controller boundary

Canonical archived manifest:
`agents/runs/20261030T044705Z-build-skills/manifest.json`.
Both skill-local.md and skill-live.md were read and matched SHA-256
`28ecbeeccb0c5e5d6eb541b5a5b0f88aec47b154374d909085116d34f5629199`.
The attached skill-manifest.json and skill-evidence.json preserve that evidence;
numerical-evidence.json cites the same manifest. No later divergent policy was
used. No skill, pipeline source, prompt, published table or supervisor receipt
was edited, and no commit or push was attempted.

The build fingerprint is a read-only record, not an acceptance. A critic must
use its own NUMBERDB_RUN_ID and run the fingerprint command again against the
live table. Include generate.py, solver.py and every other reviewed source
or evidence dependency; the build fingerprint lists the attached dependency set.
No independent critique sidecar has been fabricated by this build.

Existing tags physics and dimensionless were retained. The requested subject
tag astrophysics is still absent; T613, T614, T615, T616, T617 and T618 are six
specific destinations that support the family's tag proposal. No new tag was
created as part of this table build. No future companion T-number was invented.
The controller is responsible for the successful-build queue transition and
for offering the draft only after critique and repair.