Pith Number

pith:GTQHNANT

pith:2013:GTQHNANTEQXIFPPUOXF4OM3X7F

not attested not anchored not stored refs pending

Problem with critical Sobolev exponent and with weight

Habib Yazidi, Rejeb Hadiji

arxiv:1303.1789 v1 · 2013-03-07 · 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{GTQHNANTEQXIFPPUOXF4OM3X7F}

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	2026-05-18T03:31:33.140137Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

34e07681b3242e82bdf475cbc73377f971d525a13af784f3af3cac213221e3b0

Aliases

arxiv: 1303.1789 · arxiv_version: 1303.1789v1 · doi: 10.48550/arxiv.1303.1789 · pith_short_12: GTQHNANTEQXI · pith_short_16: GTQHNANTEQXIFPPU · pith_short_8: GTQHNANT

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/GTQHNANTEQXIFPPUOXF4OM3X7F \
  | 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: 34e07681b3242e82bdf475cbc73377f971d525a13af784f3af3cac213221e3b0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7bb1de83cd867625e5490c2e7e27871ba4bab90174378ba77d4501faae2b1b9b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2013-03-07T19:32:26Z",
    "title_canon_sha256": "46128a23c4d0b07324277e761ba24164fb44f60ad18e5bd7022277b7231744d4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1303.1789",
    "kind": "arxiv",
    "version": 1
  }
}