Pith Number

pith:PAHQAJDN

pith:2026:PAHQAJDN5AZWUCKLOQR7XM3UIM

not attested not anchored not stored refs pending

Limit shapes and harmonic tricks

Nikolai Kuchumov

arxiv:2603.21255 v2 · 2026-03-22 · 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{PAHQAJDN5AZWUCKLOQR7XM3UIM}

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	2026-05-20T00:05:43.715473Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

780f00246de8336a094b7423fbb37443263f80867e141e03a6afbd7234c23b59

Aliases

arxiv: 2603.21255 · arxiv_version: 2603.21255v2 · doi: 10.48550/arxiv.2603.21255 · pith_short_12: PAHQAJDN5AZW · pith_short_16: PAHQAJDN5AZWUCKL · pith_short_8: PAHQAJDN

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/PAHQAJDN5AZWUCKLOQR7XM3UIM \
  | 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: 780f00246de8336a094b7423fbb37443263f80867e141e03a6afbd7234c23b59

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "666062c095b60f7bef3cb41141cb6d9af117b49665b03901aa9161a67e4b4ebd",
    "cross_cats_sorted": [
      "math.MP",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2026-03-22T14:18:26Z",
    "title_canon_sha256": "490a1a8cdb01c16625e67cc9faaf5ac92c5c06ffd258c3084a8c42d1294d6459"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2603.21255",
    "kind": "arxiv",
    "version": 2
  }
}