Pith Number

pith:YKFQLOOM

pith:2011:YKFQLOOM3HR3QZQ6WTJ6R2EZBP

not attested not anchored not stored refs pending

Optimal dual frames and frame completions for majorization

Demetrio Stojanoff, Mariano A. Ruiz, Pedro G. Massey

arxiv:1108.4412 v3 · 2011-08-22 · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{YKFQLOOM3HR3QZQ6WTJ6R2EZBP}

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	2026-05-18T03:53:20.387812Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c28b05b9ccd9e3b8661eb4d3e8e8990bf4d12eba6020bfaf0ab0628fc03af8ae

Aliases

arxiv: 1108.4412 · arxiv_version: 1108.4412v3 · doi: 10.48550/arxiv.1108.4412 · pith_short_12: YKFQLOOM3HR3 · pith_short_16: YKFQLOOM3HR3QZQ6 · pith_short_8: YKFQLOOM

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/YKFQLOOM3HR3QZQ6WTJ6R2EZBP \
  | 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: c28b05b9ccd9e3b8661eb4d3e8e8990bf4d12eba6020bfaf0ab0628fc03af8ae

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4f0a5d5707273abd7a90ab6ee842951af04010e92f1547a224160aca38474328",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2011-08-22T20:00:03Z",
    "title_canon_sha256": "ed8c28bac206cb07e6f0be952dedbe5b8fcca8ec45a96f07aac3141d41bc9491"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1108.4412",
    "kind": "arxiv",
    "version": 3
  }
}