Pith Number

pith:PHXYMCNZ

pith:2012:PHXYMCNZ3RIMUOM3OEZTHI5DHO

not attested not anchored not stored refs pending

The most frequent peak set of a random permutation

Anisse Kasraoui

arxiv:1210.5869 v1 · 2012-10-22 · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PHXYMCNZ3RIMUOM3OEZTHI5DHO}

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	2026-05-18T03:42:34.861803Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

79ef8609b9dc50ca399b713333a3a33b97ebe00d0eddff261c120f224376ed38

Aliases

arxiv: 1210.5869 · arxiv_version: 1210.5869v1 · doi: 10.48550/arxiv.1210.5869 · pith_short_12: PHXYMCNZ3RIM · pith_short_16: PHXYMCNZ3RIMUOM3 · pith_short_8: PHXYMCNZ

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/PHXYMCNZ3RIMUOM3OEZTHI5DHO \
  | 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: 79ef8609b9dc50ca399b713333a3a33b97ebe00d0eddff261c120f224376ed38

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "19c8800589e713329e6556d25c7581f45c91dd94d7a7263eb7b4e4af7ea28a55",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-10-22T11:06:40Z",
    "title_canon_sha256": "5f03d49bf299a87c1984ae9ab69134302081cf7a7b44afca728df78e63eb0de2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.5869",
    "kind": "arxiv",
    "version": 1
  }
}