Pith Number

pith:4Z6HZ7EO

pith:2016:4Z6HZ7EOTSDI7XIMFCPPRQTLT4

not attested not anchored not stored refs pending

Quantum Approximate Markov Chains are Thermal

Fernando G.S.L. Brandao, Kohtaro Kato

arxiv:1609.06636 v3 · 2016-09-21 · quant-ph · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4Z6HZ7EOTSDI7XIMFCPPRQTLT4}

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

2 papers in Pith

Strong-to-Weak Spontaneous Symmetry Breaking

Conditional Independence of 1D Gibbs States with Applications to Efficient Learning

Receipt and verification

First computed	2026-07-04T23:52:41.037810Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e67c7cfc8e9c868fdd0c289ef8c26b9f0a0097dc1e322e2181e61665d9297f73

Aliases

arxiv: 1609.06636 · arxiv_version: 1609.06636v3 · doi: 10.48550/arxiv.1609.06636 · pith_short_12: 4Z6HZ7EOTSDI · pith_short_16: 4Z6HZ7EOTSDI7XIM · pith_short_8: 4Z6HZ7EO

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/4Z6HZ7EOTSDI7XIMFCPPRQTLT4 \
  | 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: e67c7cfc8e9c868fdd0c289ef8c26b9f0a0097dc1e322e2181e61665d9297f73

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f26c985654c5ff3fb94981d5e659227b3308b03c64b42777686285d5b0336699",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2016-09-21T16:57:45Z",
    "title_canon_sha256": "99d24795cec7052b10f0451cf9f9fcd1baed6bd8872997692c3889315642ba15"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1609.06636",
    "kind": "arxiv",
    "version": 3
  }
}