Pith Number

pith:4PAYFDPF

pith:2021:4PAYFDPFX56TBSK7NHJWP4CMZH

not attested not anchored not stored refs pending

Length density and numerical semigroups

Christopher O'Neill, Cole Brower, Joseph McDonough, Scott Chapman, Travis Kulhanek, Vadim Ponomarenko, Vody Pavlyuk

arxiv:2110.10618 v1 · 2021-10-20 · math.AC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4PAYFDPFX56TBSK7NHJWP4CMZH}

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	2026-07-05T03:24:19.388280Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e3c1828de5bf7d30c95f69d367f04cc9dcdb6c5f90a64e7c76c27fc45ee4c8c0

Aliases

arxiv: 2110.10618 · arxiv_version: 2110.10618v1 · doi: 10.48550/arxiv.2110.10618 · pith_short_12: 4PAYFDPFX56T · pith_short_16: 4PAYFDPFX56TBSK7 · pith_short_8: 4PAYFDPF

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/4PAYFDPFX56TBSK7NHJWP4CMZH \
  | 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: e3c1828de5bf7d30c95f69d367f04cc9dcdb6c5f90a64e7c76c27fc45ee4c8c0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "66be4ad75f4d9fc7073dae773f273bf76fe6c9eb3e2befdcb4ee8f1e49f56d0a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2021-10-20T15:20:26Z",
    "title_canon_sha256": "cc0ce9f2026a76b2e2d34fc9b04aa6fb5adb142bb069b289feea56679eb22727"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2110.10618",
    "kind": "arxiv",
    "version": 1
  }
}