Pith Number

pith:3VMHY2UV

pith:2001:3VMHY2UVUPNIBJIGHMG652J5V7

not attested not anchored not stored refs pending

A Characterization of Freeness by a Factorization Property of R-transform

Alexandru Nica, Dimitri Shlyakhtenko, Roland Speicher

arxiv:math/0101146 v1 · 2001-01-17 · math.OA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3VMHY2UVUPNIBJIGHMG652J5V7}

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	2026-05-18T01:05:37.976809Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dd587c6a95a3da80a5063b0deee93dafea2c078ef1e7c0ae073fcf092216a72b

Aliases

arxiv: math/0101146 · arxiv_version: math/0101146v1 · doi: 10.48550/arxiv.math/0101146 · pith_short_12: 3VMHY2UVUPNI · pith_short_16: 3VMHY2UVUPNIBJIG · pith_short_8: 3VMHY2UV

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/3VMHY2UVUPNIBJIGHMG652J5V7 \
  | 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: dd587c6a95a3da80a5063b0deee93dafea2c078ef1e7c0ae073fcf092216a72b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "243b316b743c06b75fa82c0a6eda315977a51a6aa6788add9030273b6dd7056a",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.OA",
    "submitted_at": "2001-01-17T21:51:19Z",
    "title_canon_sha256": "231dfd883fecb3173ad187ad4314dff45a06f60f947840c3411af65c4d877ebf"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0101146",
    "kind": "arxiv",
    "version": 1
  }
}