Pith Number

pith:3S5H3OGY

pith:2026:3S5H3OGY7YXGUR5FFY3PIW47RQ

not attested not anchored not stored refs pending

A Recursive Construction Improving the Lower Bound on the Shannon Capacity of $C_7$

Yu Gao

arxiv:2607.27869 v1 · 2026-07-30 · math.CO · cs.IT · math.IT

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3S5H3OGY7YXGUR5FFY3PIW47RQ}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-07-31T01:34:31.565463Z
Builder	pith-number-builder-2026-05-17-v1
Signature	unsigned_v0
Schema	pith-number/v1.0

Canonical hash

dcba7db8d8fe2e6a47a52e36f45b9f8c13e999e17d4319965aed5df472d43144

Aliases

arxiv: 2607.27869 · arxiv_version: 2607.27869v1 · doi: 10.48550/arxiv.2607.27869 · pith_short_12: 3S5H3OGY7YXG · pith_short_16: 3S5H3OGY7YXGUR5F · pith_short_8: 3S5H3OGY

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/3S5H3OGY7YXGUR5FFY3PIW47RQ \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: dcba7db8d8fe2e6a47a52e36f45b9f8c13e999e17d4319965aed5df472d43144

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "285c6680b4ce499f036a1f8f9f434f2569566ee1d17526901e94ded77e3b362a",
    "cross_cats_sorted": [
      "cs.IT",
      "math.IT"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-07-30T08:44:15Z",
    "title_canon_sha256": "fa2fe154d79396852fda29809446b48154870194c2d83df81001503cd8a9cf62"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.27869",
    "kind": "arxiv",
    "version": 1
  }
}