Pith Number

pith:GK7TBOJN

pith:2007:GK7TBOJN3EUVYN4WANXAG5FBFZ

not attested not anchored not stored refs pending

Upper and lower bounds on resonances for manifolds hyperbolic near infinity

David Borthwick

arxiv:0710.3894 v2 · 2007-10-22 · math.SP · 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{GK7TBOJN3EUVYN4WANXAG5FBFZ}

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	2026-05-18T04:09:14.021667Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

32bf30b92dd9295c3796036e0374a12e6d850a3269b78265454f58a6422ec8f7

Aliases

arxiv: 0710.3894 · arxiv_version: 0710.3894v2 · doi: 10.48550/arxiv.0710.3894 · pith_short_12: GK7TBOJN3EUV · pith_short_16: GK7TBOJN3EUVYN4W · pith_short_8: GK7TBOJN

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/GK7TBOJN3EUVYN4WANXAG5FBFZ \
  | 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: 32bf30b92dd9295c3796036e0374a12e6d850a3269b78265454f58a6422ec8f7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2f23c2eb0d65eac816b4cad2f50f8f4b0c769e87c3ffbc85b54c2aa26bc9f568",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "",
    "primary_cat": "math.SP",
    "submitted_at": "2007-10-22T17:02:20Z",
    "title_canon_sha256": "92a42db5312fda5e36e942a68c043e3f9bf0cb30aea1b3dd780cc3f57f442e4d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0710.3894",
    "kind": "arxiv",
    "version": 2
  }
}