Pith Number

pith:C5LSU7NS

pith:2005:C5LSU7NS73CRYP56CTNJBZEJWV

not attested not anchored not stored refs pending

Monotonic Simplification and Recognizing Exchange Reducibility

William W. Menasco

arxiv:math/0507124 v3 · 2005-07-06 · math.GT · math.GN

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{C5LSU7NS73CRYP56CTNJBZEJWV}

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	2026-05-18T04:03:45.698500Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

17572a7db2fec51c3fbe14da90e489b543103dffe7f23f503c3305c328350d71

Aliases

arxiv: math/0507124 · arxiv_version: math/0507124v3 · doi: 10.48550/arxiv.math/0507124 · pith_short_12: C5LSU7NS73CR · pith_short_16: C5LSU7NS73CRYP56 · pith_short_8: C5LSU7NS

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/C5LSU7NS73CRYP56CTNJBZEJWV \
  | 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: 17572a7db2fec51c3fbe14da90e489b543103dffe7f23f503c3305c328350d71

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d0c9206de88a702e8c13edaa8a131572458b22a9d592c615dab0307556084f49",
    "cross_cats_sorted": [
      "math.GN"
    ],
    "license": "",
    "primary_cat": "math.GT",
    "submitted_at": "2005-07-06T17:46:46Z",
    "title_canon_sha256": "3fb647f76fd0900c7ca4f8e504f9fa7b20a2e8d54b67df97a21721f4e9607d31"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0507124",
    "kind": "arxiv",
    "version": 3
  }
}