Pith Number

pith:MFNMUBVG

pith:2013:MFNMUBVGESGG7WDGAMJZALOZ7N

not attested not anchored not stored refs pending

Resultants and the Borcherds Phi-function

Ken-Ichi Yoshikawa, Shigeru Mukai, Shu Kawaguchi

arxiv:1308.6454 v1 · 2013-08-29 · 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{MFNMUBVGESGG7WDGAMJZALOZ7N}

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	2026-05-18T03:14:39.815926Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

615aca06a6248c6fd8660313902dd9fb54552f92536a895bed982d97d662278f

Aliases

arxiv: 1308.6454 · arxiv_version: 1308.6454v1 · doi: 10.48550/arxiv.1308.6454 · pith_short_12: MFNMUBVGESGG · pith_short_16: MFNMUBVGESGG7WDG · pith_short_8: MFNMUBVG

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/MFNMUBVGESGG7WDGAMJZALOZ7N \
  | 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: 615aca06a6248c6fd8660313902dd9fb54552f92536a895bed982d97d662278f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "baa1ae958f1178e6dab055d96336a68726535a99fe87eb672a2da6621abffc77",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2013-08-29T12:58:12Z",
    "title_canon_sha256": "4513679d86ba5daf21854cdfe110ede641d198fc311c93b8cb002b637f5df81c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1308.6454",
    "kind": "arxiv",
    "version": 1
  }
}