Pith Number

pith:ODKF3EUY

pith:2000:ODKF3EUYOHFFVR5YKQ5BEZ3AAQ

not attested not anchored not stored refs pending

Fourier-Mukai Transform and Mirror Symmetry for D-Branes on Elliptic Calabi-Yau

Bjorn Andreas, Daniel Hernandez Ruiperez, Gottfried Curio, Shing-Tung Yau

arxiv:math/0012196 v1 · 2000-12-20 · math.AG · hep-th

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ODKF3EUYOHFFVR5YKQ5BEZ3AAQ}

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	2026-07-04T14:34:59.583904Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

70d45d929871ca5ac7b8543a1267600429ba3e6f942a091021cad15d00232ba2

Aliases

arxiv: math/0012196 · arxiv_version: math/0012196v1 · doi: 10.48550/arxiv.math/0012196 · pith_short_12: ODKF3EUYOHFF · pith_short_16: ODKF3EUYOHFFVR5Y · pith_short_8: ODKF3EUY

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/ODKF3EUYOHFFVR5YKQ5BEZ3AAQ \
  | 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: 70d45d929871ca5ac7b8543a1267600429ba3e6f942a091021cad15d00232ba2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "06201efe4624c93e5e4400c292221090668a9b251c9998d9ac7c1509e5e1b291",
    "cross_cats_sorted": [
      "hep-th"
    ],
    "license": "",
    "primary_cat": "math.AG",
    "submitted_at": "2000-12-20T18:28:50Z",
    "title_canon_sha256": "e67bbc05021242324999bc5af49e7fae9468b8cfd71f3fdf867adbfbc68fbc38"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0012196",
    "kind": "arxiv",
    "version": 1
  }
}