Pith Number

pith:E2SZVMNP

pith:2025:E2SZVMNPPDEPSHLLYON6SGKRQZ

not attested not anchored not stored refs pending

Liouville theorem for singular solutions to nonlocal equations

Minhyun Kim, Se-Chan Lee

arxiv:2507.09587 v2 · 2025-07-13 · 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{E2SZVMNPPDEPSHLLYON6SGKRQZ}

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	2026-07-05T11:37:26.317746Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

26a59ab1af78c8f91d6bc39be919518665512251f8edcb8ee3cff694c7d4ce88

Aliases

arxiv: 2507.09587 · arxiv_version: 2507.09587v2 · doi: 10.48550/arxiv.2507.09587 · pith_short_12: E2SZVMNPPDEP · pith_short_16: E2SZVMNPPDEPSHLL · pith_short_8: E2SZVMNP

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/E2SZVMNPPDEPSHLLYON6SGKRQZ \
  | 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: 26a59ab1af78c8f91d6bc39be919518665512251f8edcb8ee3cff694c7d4ce88

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4c61fc3080c4de3e85baa2cdea71fb76d61233d14098905d26b64bbbce8c75b4",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2025-07-13T11:39:21Z",
    "title_canon_sha256": "c44ab6c3e54eac7ab05ead58b533524987c321515ab9e634369fdeaa6939f028"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.09587",
    "kind": "arxiv",
    "version": 2
  }
}