Pith Number

pith:YIXWXBUT

pith:2011:YIXWXBUTVM4IDBBHRI3YA44OSX

not attested not anchored not stored refs pending

A characterization of arithmetical invariants by the monoid of relations II: The monotone catenary degree and applications to semigroup rings

Andreas Philipp

arxiv:1104.0293 v1 · 2011-04-02 · math.NT · 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{YIXWXBUTVM4IDBBHRI3YA44OSX}

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	2026-05-18T04:25:04.283985Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c22f6b8693ab388184278a3780738e95f02126071e87670d2185d736c0f6d46f

Aliases

arxiv: 1104.0293 · arxiv_version: 1104.0293v1 · doi: 10.48550/arxiv.1104.0293 · pith_short_12: YIXWXBUTVM4I · pith_short_16: YIXWXBUTVM4IDBBH · pith_short_8: YIXWXBUT

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/YIXWXBUTVM4IDBBHRI3YA44OSX \
  | 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: c22f6b8693ab388184278a3780738e95f02126071e87670d2185d736c0f6d46f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4c2d03dafb0ce879c5723472e33f02bd09ccf7ae6796c406e95479ccec46f568",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2011-04-02T06:43:59Z",
    "title_canon_sha256": "1f27a0839a8c44db674abf2da5d503a91de4d7923e834d70df33e3eb1a581c7a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1104.0293",
    "kind": "arxiv",
    "version": 1
  }
}