Pith Number

pith:VX63RGLE

pith:2006:VX63RGLEOAW5V3EUCM4IABIQFM

not attested not anchored not stored refs pending

The local form of doubly stochastic maps and joint majorization in II$_1$ factors

Martin Argerami, Pedro Massey

arxiv:math/0606060 v1 · 2006-06-02 · math.OA · 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{VX63RGLEOAW5V3EUCM4IABIQFM}

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	2026-05-18T04:20:59.590765Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

adfdb89964702ddaec9413388005102b362315dd846086b4188da8414b8fd6ed

Aliases

arxiv: math/0606060 · arxiv_version: math/0606060v1 · doi: 10.48550/arxiv.math/0606060 · pith_short_12: VX63RGLEOAW5 · pith_short_16: VX63RGLEOAW5V3EU · pith_short_8: VX63RGLE

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/VX63RGLEOAW5V3EUCM4IABIQFM \
  | 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: adfdb89964702ddaec9413388005102b362315dd846086b4188da8414b8fd6ed

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "05c5686a092f719f82fcdf5dedad257bed66f2e2a2a387d32b63e729a0ff899f",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "",
    "primary_cat": "math.OA",
    "submitted_at": "2006-06-02T16:08:24Z",
    "title_canon_sha256": "01205e7b8b9ef57d4f0181d6d7991ca87fe121948a429b905911942ccd32de2d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0606060",
    "kind": "arxiv",
    "version": 1
  }
}