Pith Number

pith:BYJN5WCU

pith:2014:BYJN5WCUGCSBRQBMCQAZ4UTYU7

not attested not anchored not stored refs pending

A proof of the conjecture of Cohen and Mullen on sums of primitive roots

Stephen D. Cohen, Tim Trudgian, Tom\'as Oliveira e Silva

arxiv:1402.2724 v2 · 2014-02-12 · 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{BYJN5WCUGCSBRQBMCQAZ4UTYU7}

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	2026-05-18T02:56:06.226477Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0e12ded85430a418c02c14019e5278a7ec989d3ae3ea5fc00c447b1330cf0d7b

Aliases

arxiv: 1402.2724 · arxiv_version: 1402.2724v2 · doi: 10.48550/arxiv.1402.2724 · pith_short_12: BYJN5WCUGCSB · pith_short_16: BYJN5WCUGCSBRQBM · pith_short_8: BYJN5WCU

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/BYJN5WCUGCSBRQBMCQAZ4UTYU7 \
  | 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: 0e12ded85430a418c02c14019e5278a7ec989d3ae3ea5fc00c447b1330cf0d7b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "89c09ac24bcb70e212c661cc800b9aca42dc703c6450cebeeed1d1b01e0fc5b8",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2014-02-12T03:38:32Z",
    "title_canon_sha256": "3f9912ece36a52a47efb539506a03268ea60dae2f05d7a29e40bf01b818da656"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1402.2724",
    "kind": "arxiv",
    "version": 2
  }
}