Pith Number

pith:Z3W7NWMB

pith:2026:Z3W7NWMB6SPHJ7GMHI3UZ5O4HQ

not attested not anchored not stored refs pending

An isomorphism theorem for infinite reduced free products

Ilan Hirshberg, N. Christopher Phillips

arxiv:2602.10220 v2 · 2026-02-10 · 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{Z3W7NWMB6SPHJ7GMHI3UZ5O4HQ}

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	2026-06-12T01:09:22.361467Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ceedf6d981f49e74fccc3a374cf5dc3c1d44c9d6e56c4f6a3ca893d3ae0a5441

Aliases

arxiv: 2602.10220 · arxiv_version: 2602.10220v2 · doi: 10.48550/arxiv.2602.10220 · pith_short_12: Z3W7NWMB6SPH · pith_short_16: Z3W7NWMB6SPHJ7GM · pith_short_8: Z3W7NWMB

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/Z3W7NWMB6SPHJ7GMHI3UZ5O4HQ \
  | 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: ceedf6d981f49e74fccc3a374cf5dc3c1d44c9d6e56c4f6a3ca893d3ae0a5441

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d476a4d30dd0a4e2f4ca7d97d3887710b05a0689af47e213463402f5106733c5",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2026-02-10T19:12:23Z",
    "title_canon_sha256": "66b1aec4b4634e1d965a9cef094e7f20c5045a66bfedaa7d1d5eb2949dc8f851"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2602.10220",
    "kind": "arxiv",
    "version": 2
  }
}