Pith Number

pith:PYDA5AAP

pith:2015:PYDA5AAPEODIGSPZWLEUL6C7MZ

not attested not anchored not stored refs pending

Lectures on K-theoretic computations in enumerative geometry

Andrei Okounkov

arxiv:1512.07363 v2 · 2015-12-23 · math.AG · hep-th · math-ph · math.MP · math.RT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PYDA5AAPEODIGSPZWLEUL6C7MZ}

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	2026-05-18T00:53:34.787114Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7e060e800f23868349f9b2c945f85f667914a5e0b2102a2311edeaf91982dce7

Aliases

arxiv: 1512.07363 · arxiv_version: 1512.07363v2 · doi: 10.48550/arxiv.1512.07363 · pith_short_12: PYDA5AAPEODI · pith_short_16: PYDA5AAPEODIGSPZ · pith_short_8: PYDA5AAP

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/PYDA5AAPEODIGSPZWLEUL6C7MZ \
  | 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: 7e060e800f23868349f9b2c945f85f667914a5e0b2102a2311edeaf91982dce7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "aa9505a27093f980af4ecc233c729ab254cb5dcad8a72a9134009eff8d4a12b7",
    "cross_cats_sorted": [
      "hep-th",
      "math-ph",
      "math.MP",
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2015-12-23T05:50:22Z",
    "title_canon_sha256": "6e410acbfbbc2e87fb0bf9525dc6801cb37ec2535c4a90e00a4e0356deab7b6f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.07363",
    "kind": "arxiv",
    "version": 2
  }
}