Pith Number

pith:3T2GF4IN

pith:2024:3T2GF4INMRZT3PDQSOTBKCXBEN

not attested not anchored not stored refs pending

On Shusterman's Goldbach-type problem for sign patterns of the Liouville function

Alexander P. Mangerel

arxiv:2412.17199 v1 · 2024-12-23 · 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{3T2GF4INMRZT3PDQSOTBKCXBEN}

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	2026-07-05T09:53:18.847256Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dcf462f10d64733dbc7093a6150ae12375119482bbd466502c8d553c6bdecc7c

Aliases

arxiv: 2412.17199 · arxiv_version: 2412.17199v1 · doi: 10.48550/arxiv.2412.17199 · pith_short_12: 3T2GF4INMRZT · pith_short_16: 3T2GF4INMRZT3PDQ · pith_short_8: 3T2GF4IN

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/3T2GF4INMRZT3PDQSOTBKCXBEN \
  | 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: dcf462f10d64733dbc7093a6150ae12375119482bbd466502c8d553c6bdecc7c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3e4c22d1f77491f94405950d2c8a6c6038b1c87bcbfd78c0f4b34645df03a4a6",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2024-12-23T00:26:52Z",
    "title_canon_sha256": "e5b233137f58b8a1573c82b5708b3c40a4b59902920fce8b425fd686c4baeda3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2412.17199",
    "kind": "arxiv",
    "version": 1
  }
}