Pith Number

pith:KC5AP2Y5

pith:2026:KC5AP2Y5SOLDIS2TNWUVX5MRQX

not attested not anchored not stored refs pending

Multicriticality and Scaling: Mellin Spectral Theory, and the Decoupling of Geometric and Spectral Exponents

Alejandro Frank, Laurence A. Jacobs

arxiv:2606.07644 v1 · 2026-06-01 · math.GM · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{KC5AP2Y5SOLDIS2TNWUVX5MRQX}

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	2026-06-09T00:04:45.678482Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

50ba07eb1d9396344b536da95bf59185fd8b1bdd278b85a90efb31c596979269

Aliases

arxiv: 2606.07644 · arxiv_version: 2606.07644v1 · doi: 10.48550/arxiv.2606.07644 · pith_short_12: KC5AP2Y5SOLD · pith_short_16: KC5AP2Y5SOLDIS2T · pith_short_8: KC5AP2Y5

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/KC5AP2Y5SOLDIS2TNWUVX5MRQX \
  | 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: 50ba07eb1d9396344b536da95bf59185fd8b1bdd278b85a90efb31c596979269

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "009a8f7373b97276ecf46e910203c86422cd33e502e989056b3ce4739fbb20a0",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.GM",
    "submitted_at": "2026-06-01T19:39:08Z",
    "title_canon_sha256": "2806ca6068c2f1f9da879fa548600106aac76a0f86d40d8ce58a3ca62192bd74"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.07644",
    "kind": "arxiv",
    "version": 1
  }
}