Pith Number

pith:COF7HH64

pith:2015:COF7HH645C5KVEOBXYNS42YMFE

not attested not anchored not stored refs pending

Relative submajorization and its use in quantum resource theories

Joseph M. Renes

arxiv:1510.03695 v2 · 2015-10-13 · 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{COF7HH645C5KVEOBXYNS42YMFE}

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	2026-05-18T00:54:03.727206Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

138bf39fdce8baaa91c1be1b2e6b0c2916b284c81990ba229d1d6e71b9816680

Aliases

arxiv: 1510.03695 · arxiv_version: 1510.03695v2 · doi: 10.48550/arxiv.1510.03695 · pith_short_12: COF7HH645C5K · pith_short_16: COF7HH645C5KVEOB · pith_short_8: COF7HH64

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/COF7HH645C5KVEOBXYNS42YMFE \
  | 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: 138bf39fdce8baaa91c1be1b2e6b0c2916b284c81990ba229d1d6e71b9816680

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "78229f3ae26b9aaf17d98301c9008afb50120109ab294ed3c13f7e3f66ae3cb4",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2015-10-13T14:32:47Z",
    "title_canon_sha256": "0ba2b1c5f236d55c1baddf3e124f157cc99665846525b54bc4c7a307a8876a98"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1510.03695",
    "kind": "arxiv",
    "version": 2
  }
}