Pith Number

pith:ND7STBFU

pith:2007:ND7STBFU4ROYYOQ3LADSNCZXSL

not attested not anchored not stored refs pending

Lifting endomorphisms to automorphisms

Dennis Courtney, William Arveson

arxiv:math/0703115 v2 · 2007-03-04 · math.OA · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ND7STBFU4ROYYOQ3LADSNCZXSL}

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	2026-05-18T04:10:22.402191Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

68ff2984b4e45d8c3a1b5807268b3792c726407a7f31bc9b0441810483ac426c

Aliases

arxiv: math/0703115 · arxiv_version: math/0703115v2 · doi: 10.48550/arxiv.math/0703115 · pith_short_12: ND7STBFU4ROY · pith_short_16: ND7STBFU4ROYYOQ3 · pith_short_8: ND7STBFU

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/ND7STBFU4ROYYOQ3LADSNCZXSL \
  | 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: 68ff2984b4e45d8c3a1b5807268b3792c726407a7f31bc9b0441810483ac426c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a48d6cb30884821a6ab253420e5cc72460c6c358aed8a2503bce7208b1ad1905",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "",
    "primary_cat": "math.OA",
    "submitted_at": "2007-03-04T23:10:29Z",
    "title_canon_sha256": "e198531e8c77f5a55a7fc63a8edf2a6f0cc217e46c749e6cc3332d5420abe240"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0703115",
    "kind": "arxiv",
    "version": 2
  }
}