Pith Number

pith:7SMDUMWD

pith:2011:7SMDUMWD6YLJ4ZQC5ZCEHAQ6Q5

not attested not anchored not stored refs pending

Symplectic packings in dimension 4 and singular curves

Emmanuel Opshtein

arxiv:1110.2385 v1 · 2011-10-11 · 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{7SMDUMWD6YLJ4ZQC5ZCEHAQ6Q5}

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	2026-05-18T04:11:09.141879Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fc983a32c3f6169e6602ee4443821e874d2de4f76ded5e40c3bba3a8b70b6cb9

Aliases

arxiv: 1110.2385 · arxiv_version: 1110.2385v1 · doi: 10.48550/arxiv.1110.2385 · pith_short_12: 7SMDUMWD6YLJ · pith_short_16: 7SMDUMWD6YLJ4ZQC · pith_short_8: 7SMDUMWD

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/7SMDUMWD6YLJ4ZQC5ZCEHAQ6Q5 \
  | 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: fc983a32c3f6169e6602ee4443821e874d2de4f76ded5e40c3bba3a8b70b6cb9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "344b251f1d5af8fa4fa7e6269373ac409624eb6687572fb043921988112e7939",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SG",
    "submitted_at": "2011-10-11T14:22:16Z",
    "title_canon_sha256": "eb3e9601919751e5a043f15f90fb48a76f632923e720302836cf2d858128cdc4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1110.2385",
    "kind": "arxiv",
    "version": 1
  }
}