Pith Number

pith:JBVDXI36

pith:2001:JBVDXI365UUHYNIYCGTBPSB3WQ

not attested not anchored not stored refs pending

Some Liouville Theorems for the p-Laplacian

F. Demengel, I. Birindelli

arxiv:math/0106231 v1 · 2001-06-27 · 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{JBVDXI365UUHYNIYCGTBPSB3WQ}

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	2026-05-18T01:05:37.695560Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

486a3ba37eed287c351811a617c83bb415915fd8af9894557c204d03e1a81f48

Aliases

arxiv: math/0106231 · arxiv_version: math/0106231v1 · doi: 10.48550/arxiv.math/0106231 · pith_short_12: JBVDXI365UUH · pith_short_16: JBVDXI365UUHYNIY · pith_short_8: JBVDXI36

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/JBVDXI365UUHYNIYCGTBPSB3WQ \
  | 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: 486a3ba37eed287c351811a617c83bb415915fd8af9894557c204d03e1a81f48

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "599daa8b7e9633d2889acb45d688197cbbd7782ceaf0419ddf12aa0fd5ab2cfb",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.AP",
    "submitted_at": "2001-06-27T12:40:05Z",
    "title_canon_sha256": "d3aa05f49e6839621e0272e6f8a9cdb899e3c12982445af950304cc5a5c50cca"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0106231",
    "kind": "arxiv",
    "version": 1
  }
}