Pith Number

pith:P6AAOFJI

pith:2021:P6AAOFJISUDUBTP2MIB3AEPUIZ

not attested not anchored not stored refs pending

From Coupling to Spectral Independence and Blackbox Comparison with the Down-Up Walk

Kuikui Liu

arxiv:2103.11609 v2 · 2021-03-22 · cs.DM · cs.DS · math-ph · math.MP · 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{P6AAOFJISUDUBTP2MIB3AEPUIZ}

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.

Cited by

1 paper in Pith

Sequential Sweeps and High Dimensional Expansion

Receipt and verification

First computed	2026-07-05T02:58:40.655559Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7f80071528950740cdfa6203b011f44676bb02e9daf4f159b05a442f09708787

Aliases

arxiv: 2103.11609 · arxiv_version: 2103.11609v2 · doi: 10.48550/arxiv.2103.11609 · pith_short_12: P6AAOFJISUDU · pith_short_16: P6AAOFJISUDUBTP2 · pith_short_8: P6AAOFJI

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/P6AAOFJISUDUBTP2MIB3AEPUIZ \
  | 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: 7f80071528950740cdfa6203b011f44676bb02e9daf4f159b05a442f09708787

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e51826598ef31f336911055c687007bbba2bd013acdc548b1c3a350f2a7ab4b6",
    "cross_cats_sorted": [
      "cs.DS",
      "math-ph",
      "math.MP",
      "math.PR"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.DM",
    "submitted_at": "2021-03-22T06:32:11Z",
    "title_canon_sha256": "15d8e8fe669a841f7d8e112d16ce00a85d4753e01ad39feea1aa576576b853cb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2103.11609",
    "kind": "arxiv",
    "version": 2
  }
}