Pith Number

pith:S4HJPEDQ

pith:2023:S4HJPEDQ4GAOEBJ5Q3N2OID5BJ

not attested not anchored not stored refs pending

Comments on "Necessary optimality conditions of an optimization problem governed by a double phase PDE"

Nazih Abderrazzak Gadhi, Omar Benslimane

arxiv:2312.09142 v1 · 2023-12-14 · 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{S4HJPEDQ4GAOEBJ5Q3N2OID5BJ}

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	2026-07-05T07:24:14.995383Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

970e979070e180e2053d86dba7207d0a5225c4e57d98230af5cd40541e315a86

Aliases

arxiv: 2312.09142 · arxiv_version: 2312.09142v1 · doi: 10.48550/arxiv.2312.09142 · pith_short_12: S4HJPEDQ4GAO · pith_short_16: S4HJPEDQ4GAOEBJ5 · pith_short_8: S4HJPEDQ

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/S4HJPEDQ4GAOEBJ5Q3N2OID5BJ \
  | 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: 970e979070e180e2053d86dba7207d0a5225c4e57d98230af5cd40541e315a86

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b28e485063cbb731c423f6cc706475e70ab71c811f1d25558c7230fe30989734",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2023-12-14T17:12:27Z",
    "title_canon_sha256": "98f5402de39a4ada1d182ccc306c4573541de1ca3ffed8ccd143ca4454905079"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2312.09142",
    "kind": "arxiv",
    "version": 1
  }
}