# Graph immunity verification report

The full literal frozen existence question is answered affirmatively by the self-contained proof. For every n,m>=1 the graph-immunity dimension bound is attained. The proof first averages translates of a basis, proves the linear independent-representative theorem by induction, and adds a direct summand of dummy vectors to find a basis in different input fibres. Evaluation injectivity supplies the lower bound and a strict dimension count supplies the upper bound.

Detailed self-audit covers reduced-polynomial nonzeroness, translation invariance, quotient ranks in both induction cases, dummy-vector counts, distinct input fibres, threshold equality, and boundary degrees. No mathematical gap is currently identified. This is not an independent review, a machine-checked formal proof, or a novelty certificate.

Exact regression checks passed identically in normal and optimized Python: 28 complete function tables for 1<=m<=n<=7, an explicit degree-d* annihilator for each table, 1024 cube-subset density inequalities, 8192 translation rank identities, and all 105 partitions into pairs for the eight-point degree-one configuration. Every augmenting exchange is checked by exact GF(2) elimination. The script does not use floating-point arithmetic or Python assertions for correctness checks. These finite calculations are not the universal proof.

The exact source conjecture and definition were checked against five complete rendered pages in two primary PDFs. Classical ingredients and the previous matroid-union construction are attributed. The restricted availability of the 1942 and 2006 original articles is recorded in the source review; neither is represented as having been read in full.

All five final PDF pages were visually inspected. Author and affiliation layout, formula rendering, references, page breaks and English text were checked. The saved build_record.json and package-readiness.json record portable rebuild and replay results. Third-party source PDFs are not redistributed.

No DOI or public release is claimed for this local package. The unrelated pending Zenodo-origin access approval remains in force.