Pith Number

pith:JB67MZGF

pith:2015:JB67MZGFYCKAX6MOVZK7U667I3

not attested not anchored not stored refs pending

Response Operators for Markov Processes in a Finite State Space: Radius of Convergence and Link to the Response Theory for Axiom A Systems

Valerio Lucarini

arxiv:1506.07065 v2 · 2015-06-23 · cond-mat.stat-mech · nlin.CD · physics.data-an

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{JB67MZGFYCKAX6MOVZK7U667I3}

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	2026-05-18T01:22:01.385055Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

487df664c5c0940bf98eae55fa7bdf46e8be878fbbd8f2168494935d34f03f51

Aliases

arxiv: 1506.07065 · arxiv_version: 1506.07065v2 · doi: 10.48550/arxiv.1506.07065 · pith_short_12: JB67MZGFYCKA · pith_short_16: JB67MZGFYCKAX6MO · pith_short_8: JB67MZGF

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/JB67MZGFYCKAX6MOVZK7U667I3 \
  | 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: 487df664c5c0940bf98eae55fa7bdf46e8be878fbbd8f2168494935d34f03f51

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8b7d3bcb8875d18b77422f3e8df95fc5b688b7c2634e774bbd77ba48fe66d2a0",
    "cross_cats_sorted": [
      "nlin.CD",
      "physics.data-an"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cond-mat.stat-mech",
    "submitted_at": "2015-06-23T16:00:43Z",
    "title_canon_sha256": "6d6047d40737ac673dc520f950498d7a8e00910a8c8e11ab6fadcc27d7ff7649"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1506.07065",
    "kind": "arxiv",
    "version": 2
  }
}