Pith Number

pith:J3HBBDQA

pith:2016:J3HBBDQAI6DKQGC2ATI7S7ATB3

not attested not anchored not stored refs pending

NP-hard sets are not sparse unless P=NP: An exposition of a simple proof of Mahaney's Theorem, with applications

Joshua A. Grochow

arxiv:1610.05825 v1 · 2016-10-18 · cs.CC · math.CO · math.RT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{J3HBBDQAI6DKQGC2ATI7S7ATB3}

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	2026-05-18T01:01:51.005703Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4ece108e004786a8185a04d1f97c130ef7f5224b2a2ddf323e0d7b27c87840ef

Aliases

arxiv: 1610.05825 · arxiv_version: 1610.05825v1 · doi: 10.48550/arxiv.1610.05825 · pith_short_12: J3HBBDQAI6DK · pith_short_16: J3HBBDQAI6DKQGC2 · pith_short_8: J3HBBDQA

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/J3HBBDQAI6DKQGC2ATI7S7ATB3 \
  | 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: 4ece108e004786a8185a04d1f97c130ef7f5224b2a2ddf323e0d7b27c87840ef

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8aae883f1d6adb488c511054f9fa43633ea9cf22737e46d2e578e539a0ea6120",
    "cross_cats_sorted": [
      "math.CO",
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.CC",
    "submitted_at": "2016-10-18T23:01:55Z",
    "title_canon_sha256": "b29e1d3e08b9d39d4772d0a6fca4fbe6b1e51fb55d1769db5ea54348d717b819"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1610.05825",
    "kind": "arxiv",
    "version": 1
  }
}