Pith Number

pith:4BVAFXMZ

pith:2008:4BVAFXMZ6YV3B4ISX4GIFPMZDE

not attested not anchored not stored refs pending

Relatively Open Gromov-Witten Invariants for Symplectic Manifolds of Lower Dimensions

Hai-Long Her

arxiv:0808.2228 v6 · 2008-08-18 · 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{4BVAFXMZ6YV3B4ISX4GIFPMZDE}

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	2026-05-18T02:32:55.421138Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e06a02dd99f62bb0f112bf0c82bd99190d05fca27f132f872d77e7c990e1c688

Aliases

arxiv: 0808.2228 · arxiv_version: 0808.2228v6 · doi: 10.48550/arxiv.0808.2228 · pith_short_12: 4BVAFXMZ6YV3 · pith_short_16: 4BVAFXMZ6YV3B4IS · pith_short_8: 4BVAFXMZ

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/4BVAFXMZ6YV3B4ISX4GIFPMZDE \
  | 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: e06a02dd99f62bb0f112bf0c82bd99190d05fca27f132f872d77e7c990e1c688

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c92edde013391c10f879db65c900fa8535d366fef56004e4a481abc0d2770f83",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SG",
    "submitted_at": "2008-08-18T15:20:45Z",
    "title_canon_sha256": "d74377f2b2601c803c1741ddc17a77eb12276debd699d6a850b92142e4a071ef"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0808.2228",
    "kind": "arxiv",
    "version": 6
  }
}