Pith Number

pith:AAZD7JFF

pith:2015:AAZD7JFFSYM3R6FBTUGEJ46SKG

not attested not anchored not stored refs pending

Two Formulas for the BR Multiplicity

Steven L. Kleiman

arxiv:1507.08865 v2 · 2015-07-31 · math.AG · math.AC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{AAZD7JFFSYM3R6FBTUGEJ46SKG}

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	2026-05-18T01:11:55.095824Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

00323fa4a59619b8f8a19d0c44f3d251894cd7b62f72f0a44c036e5622634c00

Aliases

arxiv: 1507.08865 · arxiv_version: 1507.08865v2 · doi: 10.48550/arxiv.1507.08865 · pith_short_12: AAZD7JFFSYM3 · pith_short_16: AAZD7JFFSYM3R6FB · pith_short_8: AAZD7JFF

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/AAZD7JFFSYM3R6FBTUGEJ46SKG \
  | 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: 00323fa4a59619b8f8a19d0c44f3d251894cd7b62f72f0a44c036e5622634c00

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e00b7cfdec5a7b2aeafcb46b92ca8ac6a981ece23e75d9bd569a70a92e4c3127",
    "cross_cats_sorted": [
      "math.AC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2015-07-31T13:08:57Z",
    "title_canon_sha256": "adee1bda2b96adfd8de6d6cfaaf0a959e0b0cf59a2747b6b47a9e9f01bb0a88b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1507.08865",
    "kind": "arxiv",
    "version": 2
  }
}