Pith Number

pith:YBF56F3L

pith:2017:YBF56F3LMQI3G5QXXPACILLHKV

not attested not anchored not stored refs pending

Quantitative multiple mixing

Alexander Gorodnik, Manfred Einsiedler, Michael Bj\"orklund

arxiv:1701.00945 v2 · 2017-01-04 · math.DS · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{YBF56F3LMQI3G5QXXPACILLHKV}

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	2026-05-18T00:30:22.397813Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c04bdf176b6411b37617bbc0242d67556493886f03e812a6876c9902325c5720

Aliases

arxiv: 1701.00945 · arxiv_version: 1701.00945v2 · doi: 10.48550/arxiv.1701.00945 · pith_short_12: YBF56F3LMQI3 · pith_short_16: YBF56F3LMQI3G5QX · pith_short_8: YBF56F3L

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/YBF56F3LMQI3G5QXXPACILLHKV \
  | 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: c04bdf176b6411b37617bbc0242d67556493886f03e812a6876c9902325c5720

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a405658e820b407462380556f442440ab19920b22a1a4b37bf0483d5cf252370",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2017-01-04T09:57:08Z",
    "title_canon_sha256": "10e0ac5a2fafe8b2ba37453b68fdec7c60c6cb15ec16c5c2606458ad3aa6915c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1701.00945",
    "kind": "arxiv",
    "version": 2
  }
}