Pith Number

pith:3CRK3SP7

pith:2025:3CRK3SP7GDEMSLDA36DUP6MNXV

not attested not anchored not stored refs pending

Some Observations about the "Generalized Abundancy Index"

Shannon Starr

arxiv:2505.07051 v2 · 2025-05-11 · math.CO · math.NT · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3CRK3SP7GDEMSLDA36DUP6MNXV}

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.

Cited by

1 paper in Pith

Proof of a conjecture by Starr and log-concavity for random commuting permutations

Receipt and verification

First computed	2026-07-05T11:02:43.842151Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d8a2adc9ff30c8c92c60df8747f98dbd4bbccdbab96d1a6fdf2a775706f7c20f

Aliases

arxiv: 2505.07051 · arxiv_version: 2505.07051v2 · doi: 10.48550/arxiv.2505.07051 · pith_short_12: 3CRK3SP7GDEM · pith_short_16: 3CRK3SP7GDEMSLDA · pith_short_8: 3CRK3SP7

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/3CRK3SP7GDEMSLDA36DUP6MNXV \
  | 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: d8a2adc9ff30c8c92c60df8747f98dbd4bbccdbab96d1a6fdf2a775706f7c20f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bbad9706c0ff3c6041f0fc094575b9cdebbd9ecd30490b12df1ea24b00c90810",
    "cross_cats_sorted": [
      "math.NT",
      "math.PR"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2025-05-11T16:49:28Z",
    "title_canon_sha256": "6cfc860228a88f134a74429c857e9c9a0102e2a9839d917ec0631ec209c17ad5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2505.07051",
    "kind": "arxiv",
    "version": 2
  }
}