Pith Number

pith:R4DVWZGW

pith:2008:R4DVWZGWOJFV7SIBREYMGXE24S

not attested not anchored not stored refs pending

Pattern Rigidity in Hyperbolic Spaces: Duality and PD Subgroups

Kingshook Biswas, Mahan Mj

arxiv:0809.4449 v3 · 2008-09-25 · math.GT · 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{R4DVWZGWOJFV7SIBREYMGXE24S}

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	2026-05-18T03:57:37.552923Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8f075b64d6724b5fc9018930c35c9ae49ff950b4badb46b781926951823643ce

Aliases

arxiv: 0809.4449 · arxiv_version: 0809.4449v3 · doi: 10.48550/arxiv.0809.4449 · pith_short_12: R4DVWZGWOJFV · pith_short_16: R4DVWZGWOJFV7SIB · pith_short_8: R4DVWZGW

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/R4DVWZGWOJFV7SIBREYMGXE24S \
  | 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: 8f075b64d6724b5fc9018930c35c9ae49ff950b4badb46b781926951823643ce

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "afeca890b8b9f33cded657178a80dea96f1bbdae794e043e428d7203e9f0d546",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2008-09-25T16:32:58Z",
    "title_canon_sha256": "9fd3a4e432724ae1f509e4ee4a3397b3d1ea8261fbd20f784fe72279446336bb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0809.4449",
    "kind": "arxiv",
    "version": 3
  }
}