Pith Number

pith:GSBX6NS5

pith:2014:GSBX6NS5WYHCENOGLCYGLTYBRH

not attested not anchored not stored refs pending

Knapsack problems in products of groups

Alexander Ushakov, Andrey Nikolaev, Elizaveta Frenkel

arxiv:1408.6509 v2 · 2014-08-27 · math.GR · cs.CC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GSBX6NS5WYHCENOGLCYGLTYBRH}

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	2026-05-18T01:35:35.329676Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

34837f365db60e2235c658b065cf0189ec36d8884aab938e5e4c733bab1b7284

Aliases

arxiv: 1408.6509 · arxiv_version: 1408.6509v2 · doi: 10.48550/arxiv.1408.6509 · pith_short_12: GSBX6NS5WYHC · pith_short_16: GSBX6NS5WYHCENOG · pith_short_8: GSBX6NS5

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/GSBX6NS5WYHCENOGLCYGLTYBRH \
  | 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: 34837f365db60e2235c658b065cf0189ec36d8884aab938e5e4c733bab1b7284

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4b493a7c2e4ddc19874421541bd4882eb5f22d05f21563a2c67d0f897b86d1d8",
    "cross_cats_sorted": [
      "cs.CC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2014-08-27T19:46:14Z",
    "title_canon_sha256": "2318f3612132235700361f741f691f363d23ff232ce0b0eed7334b4b89fd15fc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1408.6509",
    "kind": "arxiv",
    "version": 2
  }
}