Pith Number

pith:RMHREHCB

pith:2021:RMHREHCBSGR3HCYYNEON3F3G5Q

not attested not anchored not stored refs pending

Average-case Speedup for Product Formulas

Chi-Fang (Anthony) Chen, Fernando G.S.L. Brand\~ao

arxiv:2111.05324 v2 · 2021-11-09 · quant-ph · math-ph · math.FA · math.MP · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{RMHREHCBSGR3HCYYNEON3F3G5Q}

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	2026-07-05T09:29:22.730921Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8b0f121c4191a3b38b18691cdd9766ec35768815b2126dec6bad0b9102ca6cf5

Aliases

arxiv: 2111.05324 · arxiv_version: 2111.05324v2 · doi: 10.48550/arxiv.2111.05324 · pith_short_12: RMHREHCBSGR3 · pith_short_16: RMHREHCBSGR3HCYY · pith_short_8: RMHREHCB

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/RMHREHCBSGR3HCYYNEON3F3G5Q \
  | 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: 8b0f121c4191a3b38b18691cdd9766ec35768815b2126dec6bad0b9102ca6cf5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "97ce9a2868490810069cfd3d35a56a5efcb3286ce4fd8687a8cf84b4d4da641d",
    "cross_cats_sorted": [
      "math-ph",
      "math.FA",
      "math.MP",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2021-11-09T18:49:48Z",
    "title_canon_sha256": "6327274691bb010efc672366d1207052246b5918b7f657499d201d5331119033"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2111.05324",
    "kind": "arxiv",
    "version": 2
  }
}