Pith Number

pith:AXD3QBNQ

pith:2018:AXD3QBNQENU4GDXAV65XQZ4AT6

not attested not anchored not stored refs pending

Local Energy Optimality of Periodic Sets

Achill Sch\"urmann, Renaud Coulangeon

arxiv:1802.02072 v1 · 2018-02-06 · math.MG · math-ph · math.MP · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{AXD3QBNQENU4GDXAV65XQZ4AT6}

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	2026-06-09T02:06:57.285947Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

05c7b805b02369c30ee0afbb7867809f82490f231fb295ebb7dfcce61db48e7b

Aliases

arxiv: 1802.02072 · arxiv_version: 1802.02072v1 · doi: 10.48550/arxiv.1802.02072 · pith_short_12: AXD3QBNQENU4 · pith_short_16: AXD3QBNQENU4GDXA · pith_short_8: AXD3QBNQ

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/AXD3QBNQENU4GDXAV65XQZ4AT6 \
  | 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: 05c7b805b02369c30ee0afbb7867809f82490f231fb295ebb7dfcce61db48e7b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4a4858c0ae9fa86417898c65dcfb461e1115eea5234e3a6d7f59da846762fbd2",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP",
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2018-02-06T17:00:48Z",
    "title_canon_sha256": "a7aac62eab10b1efdc12e944483d712b86a29a8847609f7fe4b9ce55193fce33"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1802.02072",
    "kind": "arxiv",
    "version": 1
  }
}