Pith Number

pith:MZRS7DRC

pith:2009:MZRS7DRC5P7KTGVR3GGRKH7HIR

not attested not anchored not stored refs pending

Derived equivalences of Calabi-Yau fibrations

Andrey Todorov, Cristina Martinez Ramirez

arxiv:0901.0509 v5 · 2009-01-05 · 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{MZRS7DRC5P7KTGVR3GGRKH7HIR}

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	2026-05-18T04:10:57.458465Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

66632f8e22ebfea99ab1d98d151fe744753f97d4f7ee7636677c7826097a2ee4

Aliases

arxiv: 0901.0509 · arxiv_version: 0901.0509v5 · doi: 10.48550/arxiv.0901.0509 · pith_short_12: MZRS7DRC5P7K · pith_short_16: MZRS7DRC5P7KTGVR · pith_short_8: MZRS7DRC

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/MZRS7DRC5P7KTGVR3GGRKH7HIR \
  | 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: 66632f8e22ebfea99ab1d98d151fe744753f97d4f7ee7636677c7826097a2ee4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d2bf0a0782a0017f16cf70e263fcfd7e97a2ef56ae9b5d4f4deae4f027b07e31",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2009-01-05T16:33:54Z",
    "title_canon_sha256": "cd8ccb155c84bc9107d39d68ce315288b814d225f38e33e11b511a9859eb9ea4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0901.0509",
    "kind": "arxiv",
    "version": 5
  }
}