Pith Number

pith:TC4ZN5X4

pith:2010:TC4ZN5X4XQZJUVUQGBYGRCVTQL

not attested not anchored not stored refs pending

Gamma-convergence results for phase-field approximations of the 2D-Euler Elastica Functional

Luca Mugnai

arxiv:1009.5826 v1 · 2010-09-29 · 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{TC4ZN5X4XQZJUVUQGBYGRCVTQL}

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	2026-05-18T04:40:08.820893Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

98b996f6fcbc329a56903070688ab382ed2fddb87383e86417c07b44a85fd0ff

Aliases

arxiv: 1009.5826 · arxiv_version: 1009.5826v1 · doi: 10.48550/arxiv.1009.5826 · pith_short_12: TC4ZN5X4XQZJ · pith_short_16: TC4ZN5X4XQZJUVUQ · pith_short_8: TC4ZN5X4

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/TC4ZN5X4XQZJUVUQGBYGRCVTQL \
  | 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: 98b996f6fcbc329a56903070688ab382ed2fddb87383e86417c07b44a85fd0ff

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "846b5daabbefdc450ef02356e0dedf0cb94b991482a7331f18063967b2047944",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2010-09-29T10:02:51Z",
    "title_canon_sha256": "85c550bde81ba2a4fef5b74e632b085fd3a31d0d081c7bbe9005beae2db662c6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1009.5826",
    "kind": "arxiv",
    "version": 1
  }
}