Pith Number

pith:BMK5OX3M

pith:2011:BMK5OX3MIGO5E2GNHN2PUONAOO

not attested not anchored not stored refs pending

Self cup products and the theta characteristic torsor

Bjorn Poonen, Eric Rains

arxiv:1104.2105 v1 · 2011-04-12 · math.NT · 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{BMK5OX3MIGO5E2GNHN2PUONAOO}

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	2026-05-18T00:47:34.156249Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0b15d75f6c419dd268cd3b74fa39a07390a84d2734b3acac373bcbacd6a75f15

Aliases

arxiv: 1104.2105 · arxiv_version: 1104.2105v1 · doi: 10.48550/arxiv.1104.2105 · pith_short_12: BMK5OX3MIGO5 · pith_short_16: BMK5OX3MIGO5E2GN · pith_short_8: BMK5OX3M

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/BMK5OX3MIGO5E2GNHN2PUONAOO \
  | 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: 0b15d75f6c419dd268cd3b74fa39a07390a84d2734b3acac373bcbacd6a75f15

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fab33d90336998a37e97d5b4a48e85c5aae0f2607f37f5227828e70c943ee3e4",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2011-04-12T02:56:02Z",
    "title_canon_sha256": "cafffd3b182cad26d9b0ee54d4d58208fd2a0202d457a787605e77e625e947af"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1104.2105",
    "kind": "arxiv",
    "version": 1
  }
}