Pith Number

pith:57VZGSQ7

pith:2010:57VZGSQ747P6GPYM22IIXDPPSO

not attested not anchored not stored refs pending

Mirror Symmetry for Closed, Open, and Unoriented Gromov-Witten Invariants

Aleksey Zinger, Alexandra Popa

arxiv:1010.1946 v4 · 2010-10-10 · 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{57VZGSQ747P6GPYM22IIXDPPSO}

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	2026-05-18T03:32:32.065890Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

efeb934a1fe7dfe33f0cd6908b8def939c82145364fc8508122225c47757653d

Aliases

arxiv: 1010.1946 · arxiv_version: 1010.1946v4 · doi: 10.48550/arxiv.1010.1946 · pith_short_12: 57VZGSQ747P6 · pith_short_16: 57VZGSQ747P6GPYM · pith_short_8: 57VZGSQ7

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/57VZGSQ747P6GPYM22IIXDPPSO \
  | 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: efeb934a1fe7dfe33f0cd6908b8def939c82145364fc8508122225c47757653d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6180d3f0ed32b1270ccdf3545afd9c22d198878d4cefe4de35e89eb897d2a185",
    "cross_cats_sorted": [
      "math.SG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2010-10-10T18:13:02Z",
    "title_canon_sha256": "5549a952fc9e4834630180192b08cb67ebebb569d5a81ab7beccaabcb699588f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1010.1946",
    "kind": "arxiv",
    "version": 4
  }
}