Pith Number

pith:PT4A7SNS

pith:2012:PT4A7SNS3VV7FRFMWDRLHPWCDC

not attested not anchored not stored refs pending

Subcritical and supercritical Klein-Gordon-Maxwell equations without Ambrosetti-Rabinowitz condition

Patricia L. Cunha

arxiv:1206.0495 v1 · 2012-06-03 · 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{PT4A7SNS3VV7FRFMWDRLHPWCDC}

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	2026-05-18T03:54:17.509626Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7cf80fc9b2dd6bf2c4acb0e2b3bec2189ae74e5a54af8f31212c4003c05c66ac

Aliases

arxiv: 1206.0495 · arxiv_version: 1206.0495v1 · doi: 10.48550/arxiv.1206.0495 · pith_short_12: PT4A7SNS3VV7 · pith_short_16: PT4A7SNS3VV7FRFM · pith_short_8: PT4A7SNS

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/PT4A7SNS3VV7FRFMWDRLHPWCDC \
  | 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: 7cf80fc9b2dd6bf2c4acb0e2b3bec2189ae74e5a54af8f31212c4003c05c66ac

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "281a584382b88ad7bcf8c1fec0f97778292f8e0d4bfb9ec945156d5a9aa1751c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2012-06-03T21:44:07Z",
    "title_canon_sha256": "b82e85a00202dfb70224f51fdfa5765fc50a4a1ff4433bae284574721cf6a8dc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1206.0495",
    "kind": "arxiv",
    "version": 1
  }
}