Pith Number

pith:5OEV7CUN

pith:2026:5OEV7CUNB7GDFMVJIJDU2WJWBO

not attested not anchored not stored refs pending

The Fine-Structure Hierarchy of Prime Biases and the Universal Dominance of $-1 \pmod N$

Shin-ya Koyama

arxiv:2607.28931 v1 · 2026-07-31 · 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{5OEV7CUNB7GDFMVJIJDU2WJWBO}

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	2026-08-03T01:17:31.346474Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

eb895f8a8d0fcc32b2a942474d59360b8028eab6b510395a8d60e1d5425755dd

Aliases

arxiv: 2607.28931 · arxiv_version: 2607.28931v1 · doi: 10.48550/arxiv.2607.28931 · pith_short_12: 5OEV7CUNB7GD · pith_short_16: 5OEV7CUNB7GDFMVJ · pith_short_8: 5OEV7CUN

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/5OEV7CUNB7GDFMVJIJDU2WJWBO \
  | 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: eb895f8a8d0fcc32b2a942474d59360b8028eab6b510395a8d60e1d5425755dd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6acb2a645237c35623ccf940c4a63b6f1c8d4fb7a54396ec3f08eb25ee568ec1",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2026-07-31T01:26:20Z",
    "title_canon_sha256": "f06fcd622908eb1fceeb2325feacb0901631eeea703aeec527bf000ed56fdf6f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.28931",
    "kind": "arxiv",
    "version": 1
  }
}