Pith Number

pith:EJGLWDHE

pith:2009:EJGLWDHETUXBVKRZMNCCL45MFW

not attested not anchored not stored refs pending

On Hastings' counterexamples to the minimum output entropy additivity conjecture

Fernando G.S.L. Brandao, Michal Horodecki

arxiv:0907.3210 v1 · 2009-07-19 · 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{EJGLWDHETUXBVKRZMNCCL45MFW}

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	2026-07-04T17:31:23.093399Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

224cbb0ce49d2e1aaa39634425f3ac2d804d52421870d7ebf9eef6ad756c3d01

Aliases

arxiv: 0907.3210 · arxiv_version: 0907.3210v1 · doi: 10.48550/arxiv.0907.3210 · pith_short_12: EJGLWDHETUXB · pith_short_16: EJGLWDHETUXBVKRZ · pith_short_8: EJGLWDHE

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/EJGLWDHETUXBVKRZMNCCL45MFW \
  | 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: 224cbb0ce49d2e1aaa39634425f3ac2d804d52421870d7ebf9eef6ad756c3d01

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bf7178fe7dc360fc5bd9b6b04caf81567e49c5348f63540eb02f493faea556db",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2009-07-19T12:50:38Z",
    "title_canon_sha256": "b77fdb3aaeac7a24f1eaf42142dba1df21a9956618dfff891b548c8d4c07dc5f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0907.3210",
    "kind": "arxiv",
    "version": 1
  }
}