Pith Number

pith:PCWDOV7Y

pith:2016:PCWDOV7Y2U2UMKNZJDA6I5CK2E

not attested not anchored not stored refs pending

Commensurability for certain right-angled Coxeter groups and geometric amalgams of free groups

Anne Thomas, Emily Stark, Pallavi Dani

arxiv:1610.06245 v2 · 2016-10-19 · 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{PCWDOV7Y2U2UMKNZJDA6I5CK2E}

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	2026-05-18T00:33:39.583368Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

78ac3757f8d5354629b948c1e4744ad12416b7c8d362681bfde4ec3a6345477c

Aliases

arxiv: 1610.06245 · arxiv_version: 1610.06245v2 · doi: 10.48550/arxiv.1610.06245 · pith_short_12: PCWDOV7Y2U2U · pith_short_16: PCWDOV7Y2U2UMKNZ · pith_short_8: PCWDOV7Y

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/PCWDOV7Y2U2UMKNZJDA6I5CK2E \
  | 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: 78ac3757f8d5354629b948c1e4744ad12416b7c8d362681bfde4ec3a6345477c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "be7ffa80e6711f489ae6be7896a557d4aae63a062f754eb8f9ebcf72777b0d64",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2016-10-19T23:42:31Z",
    "title_canon_sha256": "e67720c44bd64f0b8b0ece9d1744c8c8b409660be5e266964606fb54f0c0e695"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1610.06245",
    "kind": "arxiv",
    "version": 2
  }
}