Pith Number

pith:3MORIVYU

pith:2012:3MORIVYUNJAUBORVIBCSKTDEZR

not attested not anchored not stored refs pending

Homological mirror symmetry and Fourier-Mukai transform

Junwu Tu

arxiv:1201.6454 v2 · 2012-01-31 · math.SG · 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{3MORIVYUNJAUBORVIBCSKTDEZR}

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	2026-05-18T03:12:58.067428Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

db1d1457146a4140ba354045254c64cc75c7486641c2db736a762346eb1ac3a5

Aliases

arxiv: 1201.6454 · arxiv_version: 1201.6454v2 · doi: 10.48550/arxiv.1201.6454 · pith_short_12: 3MORIVYUNJAU · pith_short_16: 3MORIVYUNJAUBORV · pith_short_8: 3MORIVYU

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/3MORIVYUNJAUBORVIBCSKTDEZR \
  | 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: db1d1457146a4140ba354045254c64cc75c7486641c2db736a762346eb1ac3a5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d2a44d5be07d04d80f877f361d48a07a57ea0df7594a38b6862e5806084db789",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SG",
    "submitted_at": "2012-01-31T06:11:26Z",
    "title_canon_sha256": "a2c71f32f35f12f73a3afce00689e4d2b1a017587f8c1396d310c8b8ba1e86ca"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1201.6454",
    "kind": "arxiv",
    "version": 2
  }
}