Pith Number

pith:7AT6Z6XK

pith:2016:7AT6Z6XK3VFZ64P2QMQEXWMIBG

not attested not anchored not stored refs pending

A general formula for determinants and inverses of r-circulant matrices with third order recurrences

Emrullah Kirklar, Fatih Yilmaz

arxiv:1609.08007 v1 · 2016-09-23 · math.CO

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7AT6Z6XK3VFZ64P2QMQEXWMIBG}

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	2026-05-18T01:03:54.669171Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f827ecfaeadd4b9f71fa83204bd98809ad0e1bb621fc394bb71fdd4c13ff61e6

Aliases

arxiv: 1609.08007 · arxiv_version: 1609.08007v1 · doi: 10.48550/arxiv.1609.08007 · pith_short_12: 7AT6Z6XK3VFZ · pith_short_16: 7AT6Z6XK3VFZ64P2 · pith_short_8: 7AT6Z6XK

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/7AT6Z6XK3VFZ64P2QMQEXWMIBG \
  | 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: f827ecfaeadd4b9f71fa83204bd98809ad0e1bb621fc394bb71fdd4c13ff61e6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "05c8fd48fbf5ce4472c787284e150b439d7ff508861e3b08aa325619e6af27ac",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2016-09-23T13:01:54Z",
    "title_canon_sha256": "37efbb0a14b72fd790a1fa9f4413406d4f803f9e45b072f376093682638c668e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1609.08007",
    "kind": "arxiv",
    "version": 1
  }
}