Pith Number

pith:6TU7QGSS

pith:2026:6TU7QGSST7G42FXKVUCRMPTSJX

not attested not anchored not stored refs pending

The Threshold Theorem in Watts: Fault Tolerance as a Question About Objective Probability

Amit Hagar

arxiv:2607.22276 v1 · 2026-07-24 · quant-ph

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{6TU7QGSST7G42FXKVUCRMPTSJX}

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	2026-07-27T01:20:57.374027Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f4e9f81a529fcdcd16eaad05163e724dfd06e8e80948d1f56c9ad3a4984b40d0

Aliases

arxiv: 2607.22276 · arxiv_version: 2607.22276v1 · doi: 10.48550/arxiv.2607.22276 · pith_short_12: 6TU7QGSST7G4 · pith_short_16: 6TU7QGSST7G42FXK · pith_short_8: 6TU7QGSS

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/6TU7QGSST7G42FXKVUCRMPTSJX \
  | 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: f4e9f81a529fcdcd16eaad05163e724dfd06e8e80948d1f56c9ad3a4984b40d0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d47b7890f01fa649855cca63103d1f0f1fe1b4ec5e40308968f4aadbb447b7a3",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2026-07-24T13:14:07Z",
    "title_canon_sha256": "7b13f3b08739091cd75542b72d7f6fb67f972458244801ec2930984c07b93d44"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.22276",
    "kind": "arxiv",
    "version": 1
  }
}