Pith Number

pith:XD3JAML4

pith:2015:XD3JAML44VM36AERGFJWUWGIMZ

not attested not anchored not stored refs pending

The divisor function in arithmetic progressions modulo prime powers

Rizwanur Khan

arxiv:1510.03377 v3 · 2015-10-12 · 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{XD3JAML44VM36AERGFJWUWGIMZ}

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	2026-05-18T01:14:03.045932Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b8f690317ce559bf009131536a58c8667de8de9fb4aa69bfb3b814bd9d1eb753

Aliases

arxiv: 1510.03377 · arxiv_version: 1510.03377v3 · doi: 10.48550/arxiv.1510.03377 · pith_short_12: XD3JAML44VM3 · pith_short_16: XD3JAML44VM36AER · pith_short_8: XD3JAML4

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/XD3JAML44VM36AERGFJWUWGIMZ \
  | 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: b8f690317ce559bf009131536a58c8667de8de9fb4aa69bfb3b814bd9d1eb753

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "07ebcfcebadef8a661b69afa73a2f25460db29010ed2027e1d1b707c0db57aaa",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2015-10-12T17:57:41Z",
    "title_canon_sha256": "56968c44869c5273d7ef0442b8e3374e3933a0ba7bdf12c8bacd3705f70f6708"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1510.03377",
    "kind": "arxiv",
    "version": 3
  }
}