Pith Number

pith:Y6TTUSWH

pith:2016:Y6TTUSWH2FOT64OKB7ORVKGS4T

not attested not anchored not stored refs pending

No positive cone in a free product is regular

Susan Hermiller, Zoran Sunic

arxiv:1609.06288 v2 · 2016-09-20 · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{Y6TTUSWH2FOT64OKB7ORVKGS4T}

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	2026-05-18T00:30:32.892158Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c7a73a4ac7d15d3f71ca0fdd1aa8d2e4dd2f5e6fe2659996c4f29ded1d2ba00b

Aliases

arxiv: 1609.06288 · arxiv_version: 1609.06288v2 · doi: 10.48550/arxiv.1609.06288 · pith_short_12: Y6TTUSWH2FOT · pith_short_16: Y6TTUSWH2FOT64OK · pith_short_8: Y6TTUSWH

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/Y6TTUSWH2FOT64OKB7ORVKGS4T \
  | 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: c7a73a4ac7d15d3f71ca0fdd1aa8d2e4dd2f5e6fe2659996c4f29ded1d2ba00b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e780b405ada5b2d15c87cf6bafbe7441401d31e0f8d5d57973f9240b66ac1c7b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2016-09-20T18:45:46Z",
    "title_canon_sha256": "6662e9214cc820d8a118776b09dbbaad0a2e9b6741efcf203ba1c937c26bd64f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1609.06288",
    "kind": "arxiv",
    "version": 2
  }
}