Pith Number

pith:GUWXD6LI

pith:1998:GUWXD6LIC4L42H67GSX7XS2OXZ

not attested not anchored not stored refs pending

Primitive Forms, Topological LG models coupled to Gravity and Mirror Symmetry

Atsushi Takahashi

arxiv:math/9802059 v1 · 1998-02-12 · 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{GUWXD6LIC4L42H67GSX7XS2OXZ}

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

Landau-Ginzburg-Saito theory for descendant Gromov-Witten theory on projective line

Receipt and verification

First computed	2026-07-04T14:40:26.958308Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

352d71f9681717cd1fdf34affbcb4ebe5f8ef1c552015dd9898970b84e02d724

Aliases

arxiv: math/9802059 · arxiv_version: math/9802059v1 · doi: 10.48550/arxiv.math/9802059 · pith_short_12: GUWXD6LIC4L4 · pith_short_16: GUWXD6LIC4L42H67 · pith_short_8: GUWXD6LI

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/GUWXD6LIC4L42H67GSX7XS2OXZ \
  | 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: 352d71f9681717cd1fdf34affbcb4ebe5f8ef1c552015dd9898970b84e02d724

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9d479db4c53ccc100ea7cdd3e4e8eece35c4a7b183560cb8de190e9d0b2d7e8d",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.AG",
    "submitted_at": "1998-02-12T06:49:07Z",
    "title_canon_sha256": "d79a67d7053029353a22bb5db1b313dd33979e488472f04f208ca3d98c98665e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/9802059",
    "kind": "arxiv",
    "version": 1
  }
}