Pith Number

pith:ABC4FGBJ

pith:2007:ABC4FGBJO4LWIAGTJ3D2LYNTNZ

not attested not anchored not stored refs pending

Proper actions and proper invariant metrics

Antonios Manoussos, Gennady Noskov, Herbert Abels

arxiv:math/0702322 v2 · 2007-02-12 · math.MG · 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{ABC4FGBJO4LWIAGTJ3D2LYNTNZ}

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	2026-05-18T02:57:45.277610Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0045c2982977176400d34ec7a5e1b36e780de8ce94929292bad419895c51cf77

Aliases

arxiv: math/0702322 · arxiv_version: math/0702322v2 · doi: 10.48550/arxiv.math/0702322 · pith_short_12: ABC4FGBJO4LW · pith_short_16: ABC4FGBJO4LWIAGT · pith_short_8: ABC4FGBJ

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/ABC4FGBJO4LWIAGTJ3D2LYNTNZ \
  | 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: 0045c2982977176400d34ec7a5e1b36e780de8ce94929292bad419895c51cf77

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9bd638bb8d6bf14cf2e695085f48f8f93e9609ebd9342a8925fabad7fb17d7e6",
    "cross_cats_sorted": [
      "math.GN"
    ],
    "license": "",
    "primary_cat": "math.MG",
    "submitted_at": "2007-02-12T11:51:00Z",
    "title_canon_sha256": "298820f0e02a0504636c0eed6b6d9a38b86f02db332cc86d09d691ff21933b98"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0702322",
    "kind": "arxiv",
    "version": 2
  }
}