Pith Number

pith:5PBE3VCG

pith:2026:5PBE3VCG2GN4TBGLTQNJY4KGAI

not attested not anchored not stored refs pending

Improved lower bounds for the Shannon capacity of odd cycles

Chase Carstensen, Christopher D. Rosin, Daniel Reichman, Nathaniel Itty

arxiv:2607.21517 v1 · 2026-07-23 · cs.IT · cs.AI · cs.DM · math.CO · 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{5PBE3VCG2GN4TBGLTQNJY4KGAI}

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	2026-07-24T01:24:37.350645Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ebc24dd446d19bc984cb9c1a9c7146020d0704ef8353b3553dc28295703f8046

Aliases

arxiv: 2607.21517 · arxiv_version: 2607.21517v1 · doi: 10.48550/arxiv.2607.21517 · pith_short_12: 5PBE3VCG2GN4 · pith_short_16: 5PBE3VCG2GN4TBGL · pith_short_8: 5PBE3VCG

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/5PBE3VCG2GN4TBGLTQNJY4KGAI \
  | 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: ebc24dd446d19bc984cb9c1a9c7146020d0704ef8353b3553dc28295703f8046

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f21bcb41ad46944db2f8431d50f670c890adf3f5d20d29cf3e643138681e6fc3",
    "cross_cats_sorted": [
      "cs.AI",
      "cs.DM",
      "math.CO",
      "math.IT"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.IT",
    "submitted_at": "2026-07-23T17:01:36Z",
    "title_canon_sha256": "86a0a1357f4db95d703b0452fd9393d092fd4f2cb4d1e0ebbba4927053d2ba1b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.21517",
    "kind": "arxiv",
    "version": 1
  }
}