Pith Number

pith:T5Z2HRTF

pith:2012:T5Z2HRTFOUBSSJPGN2PB7O3A56

not attested not anchored not stored refs pending

Quasi-inverse endomorphisms

A. Caranti

arxiv:1212.2554 v2 · 2012-12-11 · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{T5Z2HRTFOUBSSJPGN2PB7O3A56}

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	2026-05-18T02:27:05.991936Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9f73a3c66575032925e66e9e1fbb60ef914f5dd45a80bbbbf0e9fdf30d81a189

Aliases

arxiv: 1212.2554 · arxiv_version: 1212.2554v2 · doi: 10.48550/arxiv.1212.2554 · pith_short_12: T5Z2HRTFOUBS · pith_short_16: T5Z2HRTFOUBSSJPG · pith_short_8: T5Z2HRTF

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/T5Z2HRTFOUBSSJPGN2PB7O3A56 \
  | 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: 9f73a3c66575032925e66e9e1fbb60ef914f5dd45a80bbbbf0e9fdf30d81a189

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f3cf140e56a841821db98f4ecd9a92ab204e89a9cf9d53be496b580b15e0edff",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2012-12-11T17:45:39Z",
    "title_canon_sha256": "a7e710f8e47a7fc99ca17e2ab9e6b1c6708ad67b8e0bb434e864f031fc2b0067"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1212.2554",
    "kind": "arxiv",
    "version": 2
  }
}