Pith Number

pith:TGBYIQ3T

pith:2013:TGBYIQ3T5WERAFUWMVUSLOTNFY

not attested not anchored not stored refs pending

Helmholtz equation in unbounded domains: some convergence results for a constrained optimization problem

Giulio Ciraolo

arxiv:1307.1260 v2 · 2013-07-04 · 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{TGBYIQ3T5WERAFUWMVUSLOTNFY}

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	2026-05-18T02:29:53.266894Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9983844373ed89101696656925ba6d2e20da85d8b65fb5b45480d593e33a86f5

Aliases

arxiv: 1307.1260 · arxiv_version: 1307.1260v2 · doi: 10.48550/arxiv.1307.1260 · pith_short_12: TGBYIQ3T5WER · pith_short_16: TGBYIQ3T5WERAFUW · pith_short_8: TGBYIQ3T

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/TGBYIQ3T5WERAFUWMVUSLOTNFY \
  | 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: 9983844373ed89101696656925ba6d2e20da85d8b65fb5b45480d593e33a86f5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ab7ad4bb47b39b937631a90b585aca27708df653621e7b0bf2e0597fe9364510",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2013-07-04T10:15:05Z",
    "title_canon_sha256": "af6b01b5fa79302282513d4d315257b35521773c959729f50874cc74297d54b6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1307.1260",
    "kind": "arxiv",
    "version": 2
  }
}