Pith Number

pith:TNIQ2N54

pith:2012:TNIQ2N54B66YIMOGWHNV3VACIG

not attested not anchored not stored refs pending

Riemann Zeroes and Phase Transitions via the Spectral Operator on Fractal Strings

Hafedh Herichi, Michel L. Lapidus

arxiv:1203.4828 v2 · 2012-03-21 · math-ph · math.FA · 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{TNIQ2N54B66YIMOGWHNV3VACIG}

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	2026-05-18T01:58:04.834594Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9b510d37bc0fbd8431c6b1db5dd402418547cba53ec4339b0202f29f0b1e7bdb

Aliases

arxiv: 1203.4828 · arxiv_version: 1203.4828v2 · doi: 10.48550/arxiv.1203.4828 · pith_short_12: TNIQ2N54B66Y · pith_short_16: TNIQ2N54B66YIMOG · pith_short_8: TNIQ2N54

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/TNIQ2N54B66YIMOGWHNV3VACIG \
  | 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: 9b510d37bc0fbd8431c6b1db5dd402418547cba53ec4339b0202f29f0b1e7bdb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d5bdb8cb20bf85a7cc2ba8655eba91098cc2d48a9d61d5350d6f3e87d297f412",
    "cross_cats_sorted": [
      "math.FA",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2012-03-21T20:26:33Z",
    "title_canon_sha256": "9ddb7342b7d539a0372ce031781e4616eb18e0f315d4584c8b352141b4966965"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1203.4828",
    "kind": "arxiv",
    "version": 2
  }
}