Pith Number

pith:JDZJI4JH

pith:2018:JDZJI4JHSYBUF3JGLH7LPUAOWU

not attested not anchored not stored refs pending

Product-free sets in the free semigroup

Bhargav Narayanan, Imre Leader, Mark Walters, Shoham Letzter

arxiv:1812.04749 v1 · 2018-12-12 · 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{JDZJI4JHSYBUF3JGLH7LPUAOWU}

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	2026-05-17T23:58:29.597679Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

48f2947127960342ed2659feb7d00eb532f31afe57b562afdf4e1f19ce85d616

Aliases

arxiv: 1812.04749 · arxiv_version: 1812.04749v1 · doi: 10.48550/arxiv.1812.04749 · pith_short_12: JDZJI4JHSYBU · pith_short_16: JDZJI4JHSYBUF3JG · pith_short_8: JDZJI4JH

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/JDZJI4JHSYBUF3JGLH7LPUAOWU \
  | 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: 48f2947127960342ed2659feb7d00eb532f31afe57b562afdf4e1f19ce85d616

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9a206aa2b14d4a5bbbd5aeb65f56e90f96f4822826de845b7086a58400001f84",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2018-12-12T00:04:47Z",
    "title_canon_sha256": "71465ab90678bd7058d737093cefcc21ff2b13fa71787230ce9b874d885833cd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1812.04749",
    "kind": "arxiv",
    "version": 1
  }
}