Pith Number

pith:WFSKFFA4

pith:2008:WFSKFFA43ICUYIP4SQ2AKVWM4C

not attested not anchored not stored refs pending

T-Duality and Homological Mirror Symmetry of Toric Varieties

Bohan Fang, Chiu-Chu Melissa Liu, David Treumann, Eric Zaslow

arxiv:0811.1228 v4 · 2008-11-09 · math.AG · math.SG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{WFSKFFA43ICUYIP4SQ2AKVWM4C}

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	2026-05-18T02:54:47.642782Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b164a2941cda054c21fc94340556cce0b0710531443e79dc486c6a89a67b5dc9

Aliases

arxiv: 0811.1228 · arxiv_version: 0811.1228v4 · doi: 10.48550/arxiv.0811.1228 · pith_short_12: WFSKFFA43ICU · pith_short_16: WFSKFFA43ICUYIP4 · pith_short_8: WFSKFFA4

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/WFSKFFA43ICUYIP4SQ2AKVWM4C \
  | 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: b164a2941cda054c21fc94340556cce0b0710531443e79dc486c6a89a67b5dc9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3bd1f8eef9b9492f5f061f01388939aa8b1ad0feeb1f6f23dfb29e042010f98c",
    "cross_cats_sorted": [
      "math.SG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2008-11-09T22:56:57Z",
    "title_canon_sha256": "212b1074cc302f769498166cf3ef1b52e385e80000154491343f074f9f25b175"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0811.1228",
    "kind": "arxiv",
    "version": 4
  }
}