Pith Number

pith:OZG37IAS

pith:2007:OZG37IASORMIGFXRNJ64F4FLGQ

not attested not anchored not stored refs pending

Residue Classes Having Tardy Totients

Florian Luca, John Friedlander

arxiv:0709.3056 v1 · 2007-09-19 · 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{OZG37IASORMIGFXRNJ64F4FLGQ}

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	2026-05-18T02:58:12.297517Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

764dbfa01274588316f16a7dc2f0ab343f49858ed51753679d3e73784a6c3deb

Aliases

arxiv: 0709.3056 · arxiv_version: 0709.3056v1 · doi: 10.48550/arxiv.0709.3056 · pith_short_12: OZG37IASORMI · pith_short_16: OZG37IASORMIGFXR · pith_short_8: OZG37IAS

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/OZG37IASORMIGFXRNJ64F4FLGQ \
  | 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: 764dbfa01274588316f16a7dc2f0ab343f49858ed51753679d3e73784a6c3deb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f5905ac1df8ba27827a9b0758c43ea4fbb832f7b85e3242740a501de38d16242",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.NT",
    "submitted_at": "2007-09-19T16:10:51Z",
    "title_canon_sha256": "dc52e8219daa8b8d08a41be8e2fef867cfdc3bd5a3dfe08290b0ba64177333b8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0709.3056",
    "kind": "arxiv",
    "version": 1
  }
}