Pith Number

pith:TFWO7MIV

pith:2016:TFWO7MIVR67JIL6YXZ5VJXUJZP

not attested not anchored not stored refs pending

The Complexity of Knapsack in Graph Groups

Georg Zetzsche, Markus Lohrey

arxiv:1610.00373 v2 · 2016-10-03 · 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{TFWO7MIVR67JIL6YXZ5VJXUJZP}

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	2026-05-18T01:02:21.947987Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

996cefb1158fbe942fd8be7b54de89cbf1e3fff2d2e10d7a397065aa09ddf7d2

Aliases

arxiv: 1610.00373 · arxiv_version: 1610.00373v2 · doi: 10.48550/arxiv.1610.00373 · pith_short_12: TFWO7MIVR67J · pith_short_16: TFWO7MIVR67JIL6Y · pith_short_8: TFWO7MIV

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/TFWO7MIVR67JIL6YXZ5VJXUJZP \
  | 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: 996cefb1158fbe942fd8be7b54de89cbf1e3fff2d2e10d7a397065aa09ddf7d2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3cff6f32cb2ceb5ee6c7f85c880ed0b5ff02afc1514addcb5374a7834e9e340a",
    "cross_cats_sorted": [
      "cs.CC"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2016-10-03T00:05:08Z",
    "title_canon_sha256": "3d884c0cd44749bf233a7e214816c9adce1d2314bdbac72dfeaf224c8bb0b9f2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1610.00373",
    "kind": "arxiv",
    "version": 2
  }
}