Pith Number

pith:TZJUK5WN

pith:2013:TZJUK5WNG677O3PHFGAJF5YRXR

not attested not anchored not stored refs pending

Wieferich pairs and Barker sequences, II

Michael J. Mossinghoff, Peter Borwein

arxiv:1306.0045 v2 · 2013-05-31 · math.CO · 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{TZJUK5WNG677O3PHFGAJF5YRXR}

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	2026-05-17T23:53:35.582955Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9e534576cd37bff76de7298092f711bc79a94d1d59e9b061cc6ca2b9677481f0

Aliases

arxiv: 1306.0045 · arxiv_version: 1306.0045v2 · doi: 10.48550/arxiv.1306.0045 · pith_short_12: TZJUK5WNG677 · pith_short_16: TZJUK5WNG677O3PH · pith_short_8: TZJUK5WN

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/TZJUK5WNG677O3PHFGAJF5YRXR \
  | 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: 9e534576cd37bff76de7298092f711bc79a94d1d59e9b061cc6ca2b9677481f0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e14cb6d4e0d01193286b64e3d08c3d00e4e3e6a2b51ba9dcf7df0c613136c11f",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2013-05-31T22:51:23Z",
    "title_canon_sha256": "676f3e57c8f14ea22329d605d4295c3634823c90338cc603eb14d684c6127ca4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1306.0045",
    "kind": "arxiv",
    "version": 2
  }
}