Pith Number

pith:VSNMRTUW

pith:2013:VSNMRTUW7RSXRVQT65DNE42HM4

not attested not anchored not stored refs pending

Some quantitative versions of Ratner's mixing estimates

Carlos Matheus

arxiv:1312.1161 v1 · 2013-12-04 · 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{VSNMRTUW7RSXRVQT65DNE42HM4}

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	2026-05-18T03:05:34.809159Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ac9ac8ce96fc6578d613f746d2734767330231740ecc6e19ad6412d569f64378

Aliases

arxiv: 1312.1161 · arxiv_version: 1312.1161v1 · doi: 10.48550/arxiv.1312.1161 · pith_short_12: VSNMRTUW7RSX · pith_short_16: VSNMRTUW7RSXRVQT · pith_short_8: VSNMRTUW

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/VSNMRTUW7RSXRVQT65DNE42HM4 \
  | 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: ac9ac8ce96fc6578d613f746d2734767330231740ecc6e19ad6412d569f64378

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d1bc8c3b981c60e8e7bea88615eb29550f99aea91519fd03bcee6c2c96bba257",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2013-12-04T13:46:33Z",
    "title_canon_sha256": "559c7efd55d796d38c79734a7037825321731da0afcb5d1934363b724f9b0c1f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1312.1161",
    "kind": "arxiv",
    "version": 1
  }
}