Pith Number

pith:POP5F4YF

pith:2025:POP5F4YFNFGAR3JLZ2TXYWCQNA

not attested not anchored not stored refs pending

Notes on sum-free sets in abelian groups

Andrew Treglown, Nathana\"el Hassler

arxiv:2506.17401 v2 · 2025-06-20 · math.CO · math.GR · 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{POP5F4YFNFGAR3JLZ2TXYWCQNA}

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	2026-05-27T01:05:35.301187Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7b9fd2f305694c08ed2bcea77c5850683189bf38f971b316b6b1236503c09176

Aliases

arxiv: 2506.17401 · arxiv_version: 2506.17401v2 · doi: 10.48550/arxiv.2506.17401 · pith_short_12: POP5F4YFNFGA · pith_short_16: POP5F4YFNFGAR3JL · pith_short_8: POP5F4YF

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/POP5F4YFNFGAR3JLZ2TXYWCQNA \
  | 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: 7b9fd2f305694c08ed2bcea77c5850683189bf38f971b316b6b1236503c09176

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "11307913addd2ac65d3ad82e4f4f6e7532416c6caca9a672a759c32d480cba6b",
    "cross_cats_sorted": [
      "math.GR",
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2025-06-20T18:04:34Z",
    "title_canon_sha256": "8c22cc267d7620e31a080f01a37678aca22def02cf49fea9f3d5ec4576282fe7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2506.17401",
    "kind": "arxiv",
    "version": 2
  }
}