Pith Number

pith:CPGV4JQ2

pith:2012:CPGV4JQ2MU57XJXN4UPMJWHAHH

not attested not anchored not stored refs pending

A new symmetry criterion based on the distance function and applications to PDE's

Graziano Crasta, Ilaria Fragal\`a

arxiv:1207.6344 v1 · 2012-07-26 · math.AP · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CPGV4JQ2MU57XJXN4UPMJWHAHH}

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	2026-05-18T01:24:44.120159Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

13cd5e261a653bfba6ede51ec4d8e039e7d704257d730a628025d2a7e5b011b4

Aliases

arxiv: 1207.6344 · arxiv_version: 1207.6344v1 · doi: 10.48550/arxiv.1207.6344 · pith_short_12: CPGV4JQ2MU57 · pith_short_16: CPGV4JQ2MU57XJXN · pith_short_8: CPGV4JQ2

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/CPGV4JQ2MU57XJXN4UPMJWHAHH \
  | 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: 13cd5e261a653bfba6ede51ec4d8e039e7d704257d730a628025d2a7e5b011b4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "20f7863aacea86a8a17925e4ac45d8d104e7991da16e0b85922b945c3b931235",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2012-07-26T17:38:28Z",
    "title_canon_sha256": "3cbc37aaa378845239196022e5a299e5f3a9315b5f7b6fbe89cc6a3b60a60656"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1207.6344",
    "kind": "arxiv",
    "version": 1
  }
}