Pith Number

pith:AZ24CPQ6

pith:2020:AZ24CPQ6U3FKZQATREYSDWBJZR

not attested not anchored not stored refs pending

The feasible region for consecutive patterns of permutations is a cycle polytope

Jacopo Borga, Raul Penaguiao

arxiv:2003.12661 v2 · 2020-03-27 · math.CO · 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{AZ24CPQ6U3FKZQATREYSDWBJZR}

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	2026-07-05T01:49:50.630788Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0675c13e1ea6caacc013893121d829cc5ab2fd110992cd7b9b9ee968093d20fc

Aliases

arxiv: 2003.12661 · arxiv_version: 2003.12661v2 · doi: 10.48550/arxiv.2003.12661 · pith_short_12: AZ24CPQ6U3FK · pith_short_16: AZ24CPQ6U3FKZQAT · pith_short_8: AZ24CPQ6

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/AZ24CPQ6U3FKZQATREYSDWBJZR \
  | 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: 0675c13e1ea6caacc013893121d829cc5ab2fd110992cd7b9b9ee968093d20fc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "85b1632bc27c983bce9c2ad7732d4717fa9b5cc2419f3390b00c581572651c8e",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2020-03-27T22:50:14Z",
    "title_canon_sha256": "b063beb074ad55da7a4d9c2075e5541ec9e1a5feae84459669f6d38a7bdbdab7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2003.12661",
    "kind": "arxiv",
    "version": 2
  }
}