Pith Number

pith:C4WSWIXV

pith:2015:C4WSWIXVDILDMH7PGB7XMOBGZ2

not attested not anchored not stored refs pending

On periodic critical points and local minimizers of the Ohta-Kawasaki functional

Riccardo Cristoferi

arxiv:1511.04956 v3 · 2015-11-16 · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{C4WSWIXVDILDMH7PGB7XMOBGZ2}

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	2026-05-18T00:30:17.887826Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

172d2b22f51a16361fef307f763826ce87ff6c5995d9ded116f5e8dcb0fc6b12

Aliases

arxiv: 1511.04956 · arxiv_version: 1511.04956v3 · doi: 10.48550/arxiv.1511.04956 · pith_short_12: C4WSWIXVDILD · pith_short_16: C4WSWIXVDILDMH7P · pith_short_8: C4WSWIXV

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/C4WSWIXVDILDMH7PGB7XMOBGZ2 \
  | 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: 172d2b22f51a16361fef307f763826ce87ff6c5995d9ded116f5e8dcb0fc6b12

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "75599b7b0c1cd341c4ccb4ae08bb2124134a603c247e8ba0814b8d9dfc6c933a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2015-11-16T13:54:49Z",
    "title_canon_sha256": "8a307412c59bc7b1555914f138b0be1f82babade97a12b3c7839472ab642bd38"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1511.04956",
    "kind": "arxiv",
    "version": 3
  }
}