Pith Number

pith:42Y4BXCP

pith:2006:42Y4BXCPNAU2E6KX6HQ3FJ7NYA

not attested not anchored not stored refs pending

Free Entropy Dimension in Amalgamated Free Products

Kenley Jung, Kenneth J. Dykema, Nathanial P. Brown

arxiv:math/0609080 v5 · 2006-09-04 · 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{42Y4BXCPNAU2E6KX6HQ3FJ7NYA}

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	2026-05-18T02:57:45.526090Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e6b1c0dc4f6829a27957f1e1b2a7edc034a8d9eac3c76dfa829dd698df068196

Aliases

arxiv: math/0609080 · arxiv_version: math/0609080v5 · doi: 10.48550/arxiv.math/0609080 · pith_short_12: 42Y4BXCPNAU2 · pith_short_16: 42Y4BXCPNAU2E6KX · pith_short_8: 42Y4BXCP

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/42Y4BXCPNAU2E6KX6HQ3FJ7NYA \
  | 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: e6b1c0dc4f6829a27957f1e1b2a7edc034a8d9eac3c76dfa829dd698df068196

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "89b5404dd85b800edcdefb60f853c1b7e06fb92c2105327653cc307f6c858b3b",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.OA",
    "submitted_at": "2006-09-04T16:26:56Z",
    "title_canon_sha256": "f741824afee8d69efd22054e59bf66f42d1e3b9b4d4cccdbc27d93006f1ddaf9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0609080",
    "kind": "arxiv",
    "version": 5
  }
}