Pith Number

pith:KNJ74MAB

pith:2025:KNJ74MABM44KACREPYPXCJSKBK

not attested not anchored not stored refs pending

Density of spectral gap property for positively expansive dynamics and smooth potentials, with applications to the phase transition problem

Thiago Bomfim, Victor Carneiro

arxiv:2505.23934 v1 · 2025-05-29 · 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{KNJ74MABM44KACREPYPXCJSKBK}

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	2026-07-05T11:12:38.627562Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5353fe30016738a00a247e1f71264a0aba060a9c341e0cad67be68fd5c9a4fa6

Aliases

arxiv: 2505.23934 · arxiv_version: 2505.23934v1 · doi: 10.48550/arxiv.2505.23934 · pith_short_12: KNJ74MABM44K · pith_short_16: KNJ74MABM44KACRE · pith_short_8: KNJ74MAB

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/KNJ74MABM44KACREPYPXCJSKBK \
  | 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: 5353fe30016738a00a247e1f71264a0aba060a9c341e0cad67be68fd5c9a4fa6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "880670d0c18c89427c6745a4db0712df8fdb362643a7ad641a4028759d305a43",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2025-05-29T18:32:56Z",
    "title_canon_sha256": "f3d33d2a5698fe330c8692bfa9b55b38670967063f4acfada99a5a8017bc70d0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2505.23934",
    "kind": "arxiv",
    "version": 1
  }
}