Pith Number

pith:BYKG7XEH

pith:2013:BYKG7XEHVIK6KOB5KANYBMRKDR

not attested not anchored not stored refs pending

A note on sumsets of subgroups in $\mathbb Z_p^*$

Derrick Hart

arxiv:1303.2729 v2 · 2013-03-12 · 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{BYKG7XEHVIK6KOB5KANYBMRKDR}

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	2026-05-18T03:25:05.572616Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0e146fdc87aa15e5383d501b80b22a1c4811dc5a0d852528504edcf0099d92de

Aliases

arxiv: 1303.2729 · arxiv_version: 1303.2729v2 · doi: 10.48550/arxiv.1303.2729 · pith_short_12: BYKG7XEHVIK6 · pith_short_16: BYKG7XEHVIK6KOB5 · pith_short_8: BYKG7XEH

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/BYKG7XEHVIK6KOB5KANYBMRKDR \
  | 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: 0e146fdc87aa15e5383d501b80b22a1c4811dc5a0d852528504edcf0099d92de

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "924c5ffafe18d7689a0b1bf5487a28f10026f5964b5ef21f999d6ec79e19b8ef",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2013-03-12T00:15:39Z",
    "title_canon_sha256": "fa2ca413e626b2f67e7aceb22d8835e3013090ac096f7e4a7244b7ba65207de1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1303.2729",
    "kind": "arxiv",
    "version": 2
  }
}