Pith Number

pith:ZING7IR4

pith:2013:ZING7IR4CA5NWIYCPKAOMUH5H5

not attested not anchored not stored refs pending

Symplectic embeddings into four-dimensional concave toric domains

Daniel Cristofaro-Gardiner, David Frenkel, Keon Choi, Michael Hutchings, Vinicius G. B. Ramos

arxiv:1310.6647 v2 · 2013-10-24 · 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{ZING7IR4CA5NWIYCPKAOMUH5H5}

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	2026-05-18T00:44:29.402237Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ca1a6fa23c103adb23027a80e650fd3f60e165539ca5d4f56f7e24e225ab4ed1

Aliases

arxiv: 1310.6647 · arxiv_version: 1310.6647v2 · doi: 10.48550/arxiv.1310.6647 · pith_short_12: ZING7IR4CA5N · pith_short_16: ZING7IR4CA5NWIYC · pith_short_8: ZING7IR4

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/ZING7IR4CA5NWIYCPKAOMUH5H5 \
  | 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: ca1a6fa23c103adb23027a80e650fd3f60e165539ca5d4f56f7e24e225ab4ed1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0634ae43f7e35c3cf8bf2ce8b27834153dd162c24e697e176b534b409b45f132",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SG",
    "submitted_at": "2013-10-24T15:40:05Z",
    "title_canon_sha256": "0122557084bdca5f1d358dbb5311790a552a669049f9ac60f2e304f6f3000ec3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1310.6647",
    "kind": "arxiv",
    "version": 2
  }
}