Pith Number

pith:E7YLBFUI

pith:2026:E7YLBFUIQZ5W3GWI4D7AITOGZE

not attested not anchored not stored refs pending

Murmurations in the depth aspect

Catinca Mujdei, Claire Burrin, Hsin-Yi Yang, Min Lee, Vivian Kuperberg

arxiv:2603.25564 v2 · 2026-03-26 · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{E7YLBFUIQZ5W3GWI4D7AITOGZE}

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	2026-07-10T00:18:44.372642Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

27f0b09688867b6d9ac8e0fe044dc6c93b419cce058d00ae01d5ac8a5b5319d4

Aliases

arxiv: 2603.25564 · arxiv_version: 2603.25564v2 · doi: 10.48550/arxiv.2603.25564 · pith_short_12: E7YLBFUIQZ5W · pith_short_16: E7YLBFUIQZ5W3GWI · pith_short_8: E7YLBFUI

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/E7YLBFUIQZ5W3GWI4D7AITOGZE \
  | 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: 27f0b09688867b6d9ac8e0fe044dc6c93b419cce058d00ae01d5ac8a5b5319d4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b263c05724b5f55dbe6f8921c17448a97c9b2eb5560796b889545d4c1faa63f6",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2026-03-26T15:37:58Z",
    "title_canon_sha256": "a6ec34d6965043177db7857e65f2727625940eb7e4e73ec4291c33c034d95a38"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2603.25564",
    "kind": "arxiv",
    "version": 2
  }
}