Pith Number

pith:MF5P7ITM

pith:2012:MF5P7ITM4T7LH2DPEEE2MZ5Z6D

not attested not anchored not stored refs pending

Hasse theorem -- an elementary approach

Debiao He, Hao Hu, Jianhua Chen, Yitao Chen, Zhijin Hu

arxiv:1212.2535 v1 · 2012-11-27 · math.GM

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{MF5P7ITM4T7LH2DPEEE2MZ5Z6D}

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	2026-05-18T03:38:44.300380Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

617affa26ce4feb3e86f2109a667b9f0cadda60b7a3a95b5a5d6c1f21dfa81f2

Aliases

arxiv: 1212.2535 · arxiv_version: 1212.2535v1 · doi: 10.48550/arxiv.1212.2535 · pith_short_12: MF5P7ITM4T7L · pith_short_16: MF5P7ITM4T7LH2DP · pith_short_8: MF5P7ITM

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/MF5P7ITM4T7LH2DPEEE2MZ5Z6D \
  | 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: 617affa26ce4feb3e86f2109a667b9f0cadda60b7a3a95b5a5d6c1f21dfa81f2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1d6addb515723f0692d761ab53484eadbac4dfae96d02198977507a10a9fa799",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GM",
    "submitted_at": "2012-11-27T14:10:44Z",
    "title_canon_sha256": "a9893b1edb431a78016aabcec57849bdd51cfe007b7c3ceb0dd1f16a39eb128f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1212.2535",
    "kind": "arxiv",
    "version": 1
  }
}