Pith Number

pith:JFROX4T5

pith:2002:JFROX4T5Y5TWCXNGJ6KG7C53OF

not attested not anchored not stored refs pending

Dirichlet branes, homological mirror symmetry, and stability

Michael R. Douglas (Rutgers/INI/IHES)

arxiv:math/0207021 v2 · 2002-07-02 · 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{JFROX4T5Y5TWCXNGJ6KG7C53OF}

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

Stability conditions on the canonical line bundle of $\mathbb{P}^3$

Receipt and verification

First computed	2026-07-05T02:24:46.429888Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4962ebf27dc767615da64f946f8bbb71434558fabb66063bf5b9f649500f296b

Aliases

arxiv: math/0207021 · arxiv_version: math/0207021v2 · doi: 10.48550/arxiv.math/0207021 · pith_short_12: JFROX4T5Y5TW · pith_short_16: JFROX4T5Y5TWCXNG · pith_short_8: JFROX4T5

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/JFROX4T5Y5TWCXNGJ6KG7C53OF \
  | 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: 4962ebf27dc767615da64f946f8bbb71434558fabb66063bf5b9f649500f296b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3e514af519284cadac3c929271964809a7d1e406b2298e87daa9e325e3ccbd17",
    "cross_cats_sorted": [
      "hep-th"
    ],
    "license": "",
    "primary_cat": "math.AG",
    "submitted_at": "2002-07-02T16:32:57Z",
    "title_canon_sha256": "e7f4de04c43f913ef5cf308d2ff4a13d42c0d41564e0374b829c33b73873a871"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0207021",
    "kind": "arxiv",
    "version": 2
  }
}