Pith Number

pith:R5RNEU6Q

pith:2015:R5RNEU6QFMSB5KNR4FGO7AWYFH

not attested not anchored not stored refs pending

Critical non Sobolev regularity for continuity equations with rough force fields

Pierre-Emmanuel Jabin

arxiv:1507.05104 v1 · 2015-07-17 · math.AP · math.CA

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{R5RNEU6QFMSB5KNR4FGO7AWYFH}

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	2026-05-18T01:36:41.470803Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8f62d253d02b241ea9b1e14cef82d829e68f007a0940bbc03e8ad4f4bb693971

Aliases

arxiv: 1507.05104 · arxiv_version: 1507.05104v1 · doi: 10.48550/arxiv.1507.05104 · pith_short_12: R5RNEU6QFMSB · pith_short_16: R5RNEU6QFMSB5KNR · pith_short_8: R5RNEU6Q

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/R5RNEU6QFMSB5KNR4FGO7AWYFH \
  | 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: 8f62d253d02b241ea9b1e14cef82d829e68f007a0940bbc03e8ad4f4bb693971

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "91f32f5564dbac8c2ede42ff7f8a3d710c330063c533add6e0bf845e40de7d71",
    "cross_cats_sorted": [
      "math.CA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2015-07-17T20:24:30Z",
    "title_canon_sha256": "bea1aea2c4bba55286db6bbddb4f075887578139250ecab6e04c71bf69aefc65"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1507.05104",
    "kind": "arxiv",
    "version": 1
  }
}