Pith Number

pith:352OQT6R

pith:2019:352OQT6RISTJQXXBAWLTXFUJXC

not attested not anchored not stored refs pending

Automorphism-invariant positive definite functions on free groups

Beno\^it Collins, Doron Puder, Michael Magee

arxiv:1906.01518 v1 · 2019-06-04 · math.OA · math.GR · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{352OQT6RISTJQXXBAWLTXFUJXC}

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.

Cited by

1 paper in Pith

Some Orbits of Free Words that are Determined by Measures on Finite Groups

Receipt and verification

First computed	2026-07-05T02:25:15.838185Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

df74e84fd144a6985ee105973b9689b8979a4cdc4cad783d3995bfb62af847c4

Aliases

arxiv: 1906.01518 · arxiv_version: 1906.01518v1 · doi: 10.48550/arxiv.1906.01518 · pith_short_12: 352OQT6RISTJ · pith_short_16: 352OQT6RISTJQXXB · pith_short_8: 352OQT6R

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/352OQT6RISTJQXXBAWLTXFUJXC \
  | 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: df74e84fd144a6985ee105973b9689b8979a4cdc4cad783d3995bfb62af847c4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "82254bbd4c3cb9999bb8cf6a90b5446818cfe929bb44169ee7efe98e67411451",
    "cross_cats_sorted": [
      "math.GR",
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2019-06-04T15:31:22Z",
    "title_canon_sha256": "7a5f6aa8acd2cc8bbc47b2889285739cbdb3c4cf97a32ce77ca3f145aadc83e3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1906.01518",
    "kind": "arxiv",
    "version": 1
  }
}