Pith Number

pith:2IQQAKYX

pith:2004:2IQQAKYX3OO3FYYDY6DIBBIDDK

not attested not anchored not stored refs pending

Markov chains in smooth Banach spaces and Gromov hyperbolic metric spaces

Assaf Naor, Oded Schramm, Scott Sheffield, Yuval Peres

arxiv:math/0410422 v1 · 2004-10-19 · math.FA · 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{2IQQAKYX3OO3FYYDY6DIBBIDDK}

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	2026-05-18T01:05:25.726993Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d221002b17db9db2e303c7868085031aa73e031b216b9677d7664b265e64134f

Aliases

arxiv: math/0410422 · arxiv_version: math/0410422v1 · doi: 10.48550/arxiv.math/0410422 · pith_short_12: 2IQQAKYX3OO3 · pith_short_16: 2IQQAKYX3OO3FYYD · pith_short_8: 2IQQAKYX

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/2IQQAKYX3OO3FYYDY6DIBBIDDK \
  | 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: d221002b17db9db2e303c7868085031aa73e031b216b9677d7664b265e64134f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a46fa604ba65dc60e091fc1edfa1c604eb5b6f90deab54869ceefcf65fad67bc",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "",
    "primary_cat": "math.FA",
    "submitted_at": "2004-10-19T16:51:21Z",
    "title_canon_sha256": "cc28e0c81c03d99fcf3b7c794b82da5e59f232835c2546c1b2044a3d720cc58a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0410422",
    "kind": "arxiv",
    "version": 1
  }
}