Pith Number

pith:4S2RZSL3

pith:1995:4S2RZSL3VSX2CBJECJ4Y5IRPOD

not attested not anchored not stored refs pending

Volumes of Discrete Groups and Topological Complexity of Homology Spheres

Alexander Reznikov

arxiv:dg-ga/9506010 v1 · 1995-06-25 · dg-ga · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4S2RZSL3VSX2CBJECJ4Y5IRPOD}

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	2026-05-18T01:06:48.634572Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e4b51cc97bacafa1052412798ea22f70f620ce4bf5cd140508b8c8d5578d121b

Aliases

arxiv: dg-ga/9506010 · arxiv_version: dg-ga/9506010v1 · doi: 10.48550/arxiv.dg-ga/9506010 · pith_short_12: 4S2RZSL3VSX2 · pith_short_16: 4S2RZSL3VSX2CBJE · pith_short_8: 4S2RZSL3

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/4S2RZSL3VSX2CBJECJ4Y5IRPOD \
  | 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: e4b51cc97bacafa1052412798ea22f70f620ce4bf5cd140508b8c8d5578d121b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "658875e65768efd36d76aee9d5c2e27f6934a7e84e4b74f3691255f8410757e6",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "",
    "primary_cat": "dg-ga",
    "submitted_at": "1995-06-25T14:45:43Z",
    "title_canon_sha256": "b65dc29c7d34f9ccc42c2cce8286192eceba4830673b5ba14ecfc844c5568cb4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "dg-ga/9506010",
    "kind": "arxiv",
    "version": 1
  }
}