Pith Number

pith:UMFNHFSU

pith:2013:UMFNHFSU5EETTYS675UQ2HAM65

not attested not anchored not stored refs pending

Hamiltonian and Lagrangian for the trajectory of the empirical distribution and the empirical measure of Markov processes

Feijia Wang, Frank Redig

arxiv:1311.2282 v1 · 2013-11-10 · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{UMFNHFSU5EETTYS675UQ2HAM65}

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	2026-05-18T01:46:32.532728Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a30ad39654e90939e25eff690d1c0cf75c19a85378b1428fbb049d0d80bdb9d0

Aliases

arxiv: 1311.2282 · arxiv_version: 1311.2282v1 · doi: 10.48550/arxiv.1311.2282 · pith_short_12: UMFNHFSU5EET · pith_short_16: UMFNHFSU5EETTYS6 · pith_short_8: UMFNHFSU

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/UMFNHFSU5EETTYS675UQ2HAM65 \
  | 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: a30ad39654e90939e25eff690d1c0cf75c19a85378b1428fbb049d0d80bdb9d0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cb8e920386dca02cea01135fab6c7a721ba5c99f643f80b748eb5bde218392d2",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2013-11-10T16:07:25Z",
    "title_canon_sha256": "c83d0ea5109dd9302e59ca913e7aeb9392776f28a6a07ca5496156d8f0362d75"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1311.2282",
    "kind": "arxiv",
    "version": 1
  }
}