Pith Number

pith:VF7IPPSL

pith:2024:VF7IPPSL7K4IARLYVGOISTJU4P

not attested not anchored not stored refs pending

Some asymptotic results on $p$-lengths of factorizations for numerical semigroups and arithmetical congruence monoids

Christopher O'Neill, Eli B. Dugan, Emi Lycan, Sarah Mendoza De La Cruz, Shadi Gaskari, Spencer Chapman, Vadim Ponomarenko

arxiv:2411.17010 v1 · 2024-11-26 · math.AC · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VF7IPPSL7K4IARLYVGOISTJU4P}

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	2026-07-05T09:40:26.017071Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a97e87be4bfab8804578a99c894d34e3c29efa4c02b31aa84ab12c3242fdd3ec

Aliases

arxiv: 2411.17010 · arxiv_version: 2411.17010v1 · doi: 10.48550/arxiv.2411.17010 · pith_short_12: VF7IPPSL7K4I · pith_short_16: VF7IPPSL7K4IARLY · pith_short_8: VF7IPPSL

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/VF7IPPSL7K4IARLYVGOISTJU4P \
  | 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: a97e87be4bfab8804578a99c894d34e3c29efa4c02b31aa84ab12c3242fdd3ec

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "83e44cea5f45508819b11deeb0ec9cb755790851979f61a1f34693ee41f81f60",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2024-11-26T00:39:28Z",
    "title_canon_sha256": "da1ae32ff0cd193ec9f59650aae683eb06ce3a552c0da924b4950290ec2e7a9a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2411.17010",
    "kind": "arxiv",
    "version": 1
  }
}