Pith Number

pith:AWUX65J4

pith:2026:AWUX65J4ZU6XLWMM43NTZGS4QF

not attested not anchored not stored refs pending

Distributions of Inversions and Descents over Integer Compositions

E. G. Santos

arxiv:2605.20253 v1 · 2026-05-18 · math.GM

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{AWUX65J4ZU6XLWMM43NTZGS4QF}

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	2026-05-21T00:04:22.795897Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

05a97f753ccd3d75d98ce6db3c9a5c8150255177868b6fb967ec8cf4f462bcec

Aliases

arxiv: 2605.20253 · arxiv_version: 2605.20253v1 · doi: 10.48550/arxiv.2605.20253 · pith_short_12: AWUX65J4ZU6X · pith_short_16: AWUX65J4ZU6XLWMM · pith_short_8: AWUX65J4

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/AWUX65J4ZU6XLWMM43NTZGS4QF \
  | 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: 05a97f753ccd3d75d98ce6db3c9a5c8150255177868b6fb967ec8cf4f462bcec

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ec666dc7e223f9c605d1a474cd2fdc632fa7beb09bacffc139fc4822312a7397",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.GM",
    "submitted_at": "2026-05-18T11:57:23Z",
    "title_canon_sha256": "889de8406e3f66cd37825591728470a858908c6ae5ba26396f0419d1616ae7e2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.20253",
    "kind": "arxiv",
    "version": 1
  }
}