Pith Number

pith:HEYTQFRH

pith:2011:HEYTQFRHLPXUVAD3SS3N7HZC63

not attested not anchored not stored refs pending

Mirror symmetry for log Calabi-Yau surfaces I

Mark Gross, Paul Hacking, Sean Keel

arxiv:1106.4977 v3 · 2011-06-24 · 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{HEYTQFRHLPXUVAD3SS3N7HZC63}

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.

Cited by

1 paper in Pith

The Frobenius structure theorem for affine log Calabi-Yau varieties containing a torus

Receipt and verification

First computed	2026-05-18T02:25:32.940842Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

39313816275bef4a807b94b6df9f22f6dab92133e3f3b54b9f01bcb746f96b20

Aliases

arxiv: 1106.4977 · arxiv_version: 1106.4977v3 · doi: 10.48550/arxiv.1106.4977 · pith_short_12: HEYTQFRHLPXU · pith_short_16: HEYTQFRHLPXUVAD3 · pith_short_8: HEYTQFRH

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/HEYTQFRHLPXUVAD3SS3N7HZC63 \
  | 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: 39313816275bef4a807b94b6df9f22f6dab92133e3f3b54b9f01bcb746f96b20

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "af8be673faa662762892f2ec092075328838f0ae7e55bc15c5e765a3c63cbef0",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2011-06-24T14:30:19Z",
    "title_canon_sha256": "7a0b0ad079779d6e10da2fca48b00d5ced189062342432523e378e5c849ca421"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1106.4977",
    "kind": "arxiv",
    "version": 3
  }
}