Pith Number

pith:BLMNEPYE

pith:2011:BLMNEPYEGRVRQHWXQBT6WSEVZI

not attested not anchored not stored refs pending

Existence of complete Lyapunov functions for semiflows on separable metric spaces

Mauro Patr\~ao

arxiv:1107.5981 v1 · 2011-07-27 · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{BLMNEPYEGRVRQHWXQBT6WSEVZI}

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	2026-05-18T04:16:40.087366Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0ad8d23f04346b181ed78067eb4895ca1b3e992fc3866715d0a0a52d60c12611

Aliases

arxiv: 1107.5981 · arxiv_version: 1107.5981v1 · doi: 10.48550/arxiv.1107.5981 · pith_short_12: BLMNEPYEGRVR · pith_short_16: BLMNEPYEGRVRQHWX · pith_short_8: BLMNEPYE

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/BLMNEPYEGRVRQHWXQBT6WSEVZI \
  | 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: 0ad8d23f04346b181ed78067eb4895ca1b3e992fc3866715d0a0a52d60c12611

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8e060fa427c9b9d84972a52d2c17967e8bbf41a3cb0b64077bce29a6b4e4ab9f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2011-07-27T20:13:20Z",
    "title_canon_sha256": "075a62e936fc62d59d021bb03106e3e69c2a855848a3b7e50209711551c761d1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1107.5981",
    "kind": "arxiv",
    "version": 1
  }
}