Pith Number

pith:KOLRBZAA

pith:2013:KOLRBZAAB6VY7ZBPZTBJRJU35P

not attested not anchored not stored refs pending

A geometric interpretation of the Hasse-Arf theorem

Aristides Kontogeorgis

arxiv:1302.3352 v2 · 2013-02-14 · math.AG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{KOLRBZAAB6VY7ZBPZTBJRJU35P}

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	2026-05-18T03:33:25.027474Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

539710e4000fab8fe42fccc298a69bebdf0ab878eec0b2b41c1c47153963f592

Aliases

arxiv: 1302.3352 · arxiv_version: 1302.3352v2 · doi: 10.48550/arxiv.1302.3352 · pith_short_12: KOLRBZAAB6VY · pith_short_16: KOLRBZAAB6VY7ZBP · pith_short_8: KOLRBZAA

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/KOLRBZAAB6VY7ZBPZTBJRJU35P \
  | 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: 539710e4000fab8fe42fccc298a69bebdf0ab878eec0b2b41c1c47153963f592

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "74bf34b4c14a2894508f28ebf8fafaa96cab1f229aec92b09417bd9c17547531",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2013-02-14T10:05:33Z",
    "title_canon_sha256": "6d07465610e5d708b49c59542b6d4fee6654cdb382ebcc1b17f19b6e21584491"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1302.3352",
    "kind": "arxiv",
    "version": 2
  }
}