Pith Number

pith:IS22YZDI

pith:2019:IS22YZDIB5UTDRE5RAV53JXZCS

not attested not anchored not stored refs pending

Invariant systems of representatives, or The cost of symmetry

Anton A. Klyachko, Natalia M. Luneva

arxiv:1908.03315 v3 · 2019-08-09 · math.CO · math.GR

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{IS22YZDIB5UTDRE5RAV53JXZCS}

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	2026-07-05T02:21:49.728122Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

44b5ac64680f6931c49d882bdda6f9149a3ab6a4d78461051a4912da44e7cd22

Aliases

arxiv: 1908.03315 · arxiv_version: 1908.03315v3 · doi: 10.48550/arxiv.1908.03315 · pith_short_12: IS22YZDIB5UT · pith_short_16: IS22YZDIB5UTDRE5 · pith_short_8: IS22YZDI

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/IS22YZDIB5UTDRE5RAV53JXZCS \
  | 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: 44b5ac64680f6931c49d882bdda6f9149a3ab6a4d78461051a4912da44e7cd22

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1281740e4f49d15841786782a606a086fbf02e78181e5cf4116e177c0300a9e1",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2019-08-09T04:58:27Z",
    "title_canon_sha256": "bbfbd9dc72a622cbda13c994f290c28993d58bf59f1e7e4dcaf13f633142036f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1908.03315",
    "kind": "arxiv",
    "version": 3
  }
}