Pith Number

pith:GZZKUEZU

pith:2013:GZZKUEZUJFSEB7UMDLNKT4CPHQ

not attested not anchored not stored refs pending

General mixing time bounds for finite Markov chains via the absolute spectral gap

Daniel Jerison

arxiv:1310.8021 v1 · 2013-10-30 · 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{GZZKUEZUJFSEB7UMDLNKT4CPHQ}

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	2026-05-18T03:08:26.274050Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3672aa1334496440fe8c1adaa9f04f3c0734825d94917cf540bc7e6420ffb58f

Aliases

arxiv: 1310.8021 · arxiv_version: 1310.8021v1 · doi: 10.48550/arxiv.1310.8021 · pith_short_12: GZZKUEZUJFSE · pith_short_16: GZZKUEZUJFSEB7UM · pith_short_8: GZZKUEZU

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/GZZKUEZUJFSEB7UMDLNKT4CPHQ \
  | 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: 3672aa1334496440fe8c1adaa9f04f3c0734825d94917cf540bc7e6420ffb58f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4fe1d4ff2fd4859ddf1d4ea51be1abc681fc9797a138041c023f15b9da512ce6",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2013-10-30T04:58:56Z",
    "title_canon_sha256": "36add61c4f6774bc94b762f6be6b4629833f6506ad327685685d67dae864d12f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1310.8021",
    "kind": "arxiv",
    "version": 1
  }
}