Pith Number

pith:VDVQ6A75

pith:2009:VDVQ6A75NDOMOCGH2JCNBG4DVS

not attested not anchored not stored refs pending

BQP and the Polynomial Hierarchy

Scott Aaronson

arxiv:0910.4698 v1 · 2009-10-25 · quant-ph · 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{VDVQ6A75NDOMOCGH2JCNBG4DVS}

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.

Cited by

1 paper in Pith

Phase Transitions in Decision Problems Over Odd-Sized Alphabets

Receipt and verification

First computed	2026-07-04T15:57:15.258628Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a8eb0f03fd68dcc708c7d244d09b83ac8c30d635007a5c8b072269a41759bd4c

Aliases

arxiv: 0910.4698 · arxiv_version: 0910.4698v1 · doi: 10.48550/arxiv.0910.4698 · pith_short_12: VDVQ6A75NDOM · pith_short_16: VDVQ6A75NDOMOCGH · pith_short_8: VDVQ6A75

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/VDVQ6A75NDOMOCGH2JCNBG4DVS \
  | 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: a8eb0f03fd68dcc708c7d244d09b83ac8c30d635007a5c8b072269a41759bd4c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "232b1d80d309f0010b7a3a5c43d9273a9d7aa67afdde561ec42a350b3ab4ca6d",
    "cross_cats_sorted": [
      "cs.CC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2009-10-25T17:23:15Z",
    "title_canon_sha256": "07b1c4eeb4bc24a496e0834ca68f89ac67dee3b3bb65672112c89aa5cda0b242"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0910.4698",
    "kind": "arxiv",
    "version": 1
  }
}