Pith Number

pith:BSCCLSGL

pith:2022:BSCCLSGLRDVKQVHH7SQXB5EF5P

not attested not anchored not stored refs pending

Mutual Information, Information-Theoretic Thresholds and the Condensation Phenomenon at Positive Temperature

Konstantinos Panagiotou, Matija Pasch

arxiv:2207.11002 v1 · 2022-07-22 · math.CO · 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{BSCCLSGLRDVKQVHH7SQXB5EF5P}

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	2026-07-05T04:42:42.551868Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0c8425c8cb88eaa854e7fca170f485ebffaca7317ce071ae965827a611a69eb3

Aliases

arxiv: 2207.11002 · arxiv_version: 2207.11002v1 · doi: 10.48550/arxiv.2207.11002 · pith_short_12: BSCCLSGLRDVK · pith_short_16: BSCCLSGLRDVKQVHH · pith_short_8: BSCCLSGL

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/BSCCLSGLRDVKQVHH7SQXB5EF5P \
  | 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: 0c8425c8cb88eaa854e7fca170f485ebffaca7317ce071ae965827a611a69eb3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cce26e7bed6ee25f70e50431f4a9b2f0fce095f1db2e7faae63e23aa0cff3e47",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2022-07-22T10:41:41Z",
    "title_canon_sha256": "1ace3041bef087a8d5e001c843088600250e759a40870812bee36642544dae1a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2207.11002",
    "kind": "arxiv",
    "version": 1
  }
}