Pith Number

pith:6EFNPKRB

pith:2004:6EFNPKRBQXQV4TMNOYDOHMLJXD

not attested not anchored not stored refs pending

Noncommutative Poincare duality for boundary actions of hyperbolic groups

Heath Emerson

arxiv:math/0405387 v1 · 2004-05-20 · math.OA · math.KT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{6EFNPKRBQXQV4TMNOYDOHMLJXD}

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	2026-05-18T01:05:26.357046Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f10ad7aa2185e15e4d8d7606e3b169b8f50132605ec73d31dc4ee02c83a22a8b

Aliases

arxiv: math/0405387 · arxiv_version: math/0405387v1 · doi: 10.48550/arxiv.math/0405387 · pith_short_12: 6EFNPKRBQXQV · pith_short_16: 6EFNPKRBQXQV4TMN · pith_short_8: 6EFNPKRB

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/6EFNPKRBQXQV4TMNOYDOHMLJXD \
  | 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: f10ad7aa2185e15e4d8d7606e3b169b8f50132605ec73d31dc4ee02c83a22a8b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "adc448851041374d4a129104809356418c7d4189561e8a308a51bdf8defd27b3",
    "cross_cats_sorted": [
      "math.KT"
    ],
    "license": "",
    "primary_cat": "math.OA",
    "submitted_at": "2004-05-20T08:05:58Z",
    "title_canon_sha256": "af9ca244556ea3a0ce9ee68dccca9aa2dc1567fe43a3af079519b43688a83db8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0405387",
    "kind": "arxiv",
    "version": 1
  }
}