Pith Number

pith:IG5YY4VI

pith:2025:IG5YY4VIHFAGNQLYYZ4SSUCDRN

not attested not anchored not stored refs pending

A regularity theory for second-order parabolic partial differential equations in weighted mixed norm Sobolev-Zygmund spaces

Jae-Hwan Choi, Junhee Ryu

arxiv:2512.24020 v2 · 2025-12-30 · 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{IG5YY4VIHFAGNQLYYZ4SSUCDRN}

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	2026-06-04T01:09:40.636210Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

41bb8c72a8394066c178c6792950438b7a24d575ce1440de3102088c829f7313

Aliases

arxiv: 2512.24020 · arxiv_version: 2512.24020v2 · doi: 10.48550/arxiv.2512.24020 · pith_short_12: IG5YY4VIHFAG · pith_short_16: IG5YY4VIHFAGNQLY · pith_short_8: IG5YY4VI

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/IG5YY4VIHFAGNQLYYZ4SSUCDRN \
  | 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: 41bb8c72a8394066c178c6792950438b7a24d575ce1440de3102088c829f7313

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7cb1c4aab109a789da21b453afedeb5e76365384ffe837092810e070d8972125",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2025-12-30T06:42:51Z",
    "title_canon_sha256": "88b00de24e338e0b03428ca5c28ea1741c25b6700aba2b549afa16b2264c1e79"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2512.24020",
    "kind": "arxiv",
    "version": 2
  }
}