Pith Number

pith:QCZSFJX6

pith:2026:QCZSFJX6VMIYB2X6P5OFLGLWQ7

not attested not anchored not stored refs pending

Bump-Friedberg type periods beyond the cuspidal spectrum

Shenghao Li

arxiv:2607.10289 v1 · 2026-07-11 · math.RT · 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{QCZSFJX6VMIYB2X6P5OFLGLWQ7}

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	2026-07-14T01:21:07.688553Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

80b322a6feab1180eafe7f5c55997687d162acdcfe25e5828ac1750e9ee5c522

Aliases

arxiv: 2607.10289 · arxiv_version: 2607.10289v1 · doi: 10.48550/arxiv.2607.10289 · pith_short_12: QCZSFJX6VMIY · pith_short_16: QCZSFJX6VMIYB2X6 · pith_short_8: QCZSFJX6

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/QCZSFJX6VMIYB2X6P5OFLGLWQ7 \
  | 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: 80b322a6feab1180eafe7f5c55997687d162acdcfe25e5828ac1750e9ee5c522

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "14c51b1231d7aab64301939b0c8eb36f9a79f06b13a1b19265f3c6fbd7fd05f5",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.RT",
    "submitted_at": "2026-07-11T12:36:16Z",
    "title_canon_sha256": "9805b57943392aebc3f6a17a712014600396a323fd27591d15cb3a0358df6af0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.10289",
    "kind": "arxiv",
    "version": 1
  }
}