Pith Number

pith:P3IHHB6V

pith:2021:P3IHHB6VMEDDNDAPZKQ3UXCKGC

not attested not anchored not stored refs pending

Ascending chains of free subgroups in closed hyperbolic and graph 3-manifold groups

Edgar A. Bering IV, Nir Lazarovich

arxiv:2111.11777 v3 · 2021-11-23 · 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{P3IHHB6VMEDDNDAPZKQ3UXCKGC}

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	2026-06-23T02:12:29.565441Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7ed07387d56106368c0fcaa1ba5c4a30a0a856aa1a16d90ee50df204407fd96e

Aliases

arxiv: 2111.11777 · arxiv_version: 2111.11777v3 · doi: 10.48550/arxiv.2111.11777 · pith_short_12: P3IHHB6VMEDD · pith_short_16: P3IHHB6VMEDDNDAP · pith_short_8: P3IHHB6V

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/P3IHHB6VMEDDNDAPZKQ3UXCKGC \
  | 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: 7ed07387d56106368c0fcaa1ba5c4a30a0a856aa1a16d90ee50df204407fd96e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "56acf50dbb341db85770501f329057a3e2f32ba644d2c10164cef1b5cbed5d20",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2021-11-23T10:45:25Z",
    "title_canon_sha256": "6d240f940583234643609f8f064a6ef92edd6ceac1185a990c9c0056bbd2f613"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2111.11777",
    "kind": "arxiv",
    "version": 3
  }
}