Pith Number

pith:7PZSMGZY

pith:2017:7PZSMGZYZAJDMESXZHAGRKNNOX

not attested not anchored not stored refs pending

Power monoids: A bridge between Factorization Theory and Arithmetic Combinatorics

Salvatore Tringali, Yushuang Fan

arxiv:1701.09152 v6 · 2017-01-31 · math.NT · math.AC · math.CO · math.RA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7PZSMGZYZAJDMESXZHAGRKNNOX}

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	2026-05-17T23:51:06.364406Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fbf3261b38c812361257c9c068a9ad75f3131b68b9762829cb20eed3a80e1de6

Aliases

arxiv: 1701.09152 · arxiv_version: 1701.09152v6 · doi: 10.48550/arxiv.1701.09152 · pith_short_12: 7PZSMGZYZAJD · pith_short_16: 7PZSMGZYZAJDMESX · pith_short_8: 7PZSMGZY

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/7PZSMGZYZAJDMESXZHAGRKNNOX \
  | 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: fbf3261b38c812361257c9c068a9ad75f3131b68b9762829cb20eed3a80e1de6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f72d0f031030c79329d8495a64d6fd92ca4c436d389ab073b18f2c99e9e210b9",
    "cross_cats_sorted": [
      "math.AC",
      "math.CO",
      "math.RA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2017-01-31T17:50:57Z",
    "title_canon_sha256": "362feee2265112b77d48137703e383006b5adb85e5b8a8897e1997107e1af190"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1701.09152",
    "kind": "arxiv",
    "version": 6
  }
}