Pith Number

pith:ZB5JU2LU

pith:2005:ZB5JU2LUTFEYLDBZ5BMOZDMD3F

not attested not anchored not stored refs pending

Chain-rules for channel capacity

Rahul Jain

arxiv:quant-ph/0507088 v3 · 2005-07-08 · 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{ZB5JU2LUTFEYLDBZ5BMOZDMD3F}

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	2026-07-05T01:55:26.917155Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c87a9a69749949858c39e858ec8d83d9537ac66080c0eed324ef9db1564d218a

Aliases

arxiv: quant-ph/0507088 · arxiv_version: quant-ph/0507088v3 · doi: 10.48550/arxiv.quant-ph/0507088 · pith_short_12: ZB5JU2LUTFEY · pith_short_16: ZB5JU2LUTFEYLDBZ · pith_short_8: ZB5JU2LU

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/ZB5JU2LUTFEYLDBZ5BMOZDMD3F \
  | 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: c87a9a69749949858c39e858ec8d83d9537ac66080c0eed324ef9db1564d218a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "28354f57cd93fe02ee3720d2aefe068a17caeee82405a9ce745e0e5898a762c4",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2005-07-08T19:07:04Z",
    "title_canon_sha256": "885602547a6b45980bf1a76d4ddfe6bf4f3007ddc5f8f1b891c8b8bfb81f0535"
  },
  "schema_version": "1.0",
  "source": {
    "id": "quant-ph/0507088",
    "kind": "arxiv",
    "version": 3
  }
}