Pith Number

pith:5SRR67RP

pith:2015:5SRR67RPF3EAGSTVSE2FT5FF7W

not attested not anchored not stored refs pending

On Kronecker's density theorem, primitive points and orbits of matrices

Michel Laurent

arxiv:1512.00679 v1 · 2015-12-02 · 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{5SRR67RPF3EAGSTVSE2FT5FF7W}

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	2026-05-18T01:25:25.387984Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

eca31f7e2f2ec8034a75913459f4a5fdb40269697f18e47fc56c630d6733ed3a

Aliases

arxiv: 1512.00679 · arxiv_version: 1512.00679v1 · doi: 10.48550/arxiv.1512.00679 · pith_short_12: 5SRR67RPF3EA · pith_short_16: 5SRR67RPF3EAGSTV · pith_short_8: 5SRR67RP

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/5SRR67RPF3EAGSTVSE2FT5FF7W \
  | 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: eca31f7e2f2ec8034a75913459f4a5fdb40269697f18e47fc56c630d6733ed3a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "681187df9b25920301efe7185770a06cc123f3ef59c57d241845cd7f6e0a1210",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2015-12-02T13:04:04Z",
    "title_canon_sha256": "12260d5b94f0df67fd9a903e8e553b468e740e620bcd5e16cd3573397e8eee05"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.00679",
    "kind": "arxiv",
    "version": 1
  }
}