Pith Number

pith:CU6JVYW6

pith:2008:CU6JVYW6N7FNUO5IL4TBQYDL57

not attested not anchored not stored refs pending

Geodesically Complete Lorentzian Metrics on Some Homogeneous 3 Manifolds

Alberto Medina, Shirley Bromberg

arxiv:0806.1632 v3 · 2008-06-10 · 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{CU6JVYW6N7FNUO5IL4TBQYDL57}

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	2026-07-04T15:34:08.817763Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

153c9ae2de6fcada3ba85f2618606befc4af275a277fc0e634c5bef1eeb75560

Aliases

arxiv: 0806.1632 · arxiv_version: 0806.1632v3 · doi: 10.48550/arxiv.0806.1632 · pith_short_12: CU6JVYW6N7FN · pith_short_16: CU6JVYW6N7FNUO5I · pith_short_8: CU6JVYW6

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/CU6JVYW6N7FNUO5IL4TBQYDL57 \
  | 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: 153c9ae2de6fcada3ba85f2618606befc4af275a277fc0e634c5bef1eeb75560

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "462bf379669740b619e71410dc71293b01ccb19154f258c965313bd79c030710",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-nc-sa/3.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2008-06-10T10:52:32Z",
    "title_canon_sha256": "fd0882fa7a3e0d31d7d8570e1e126286b5e889aad9d8992e426c334c5a7d638a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0806.1632",
    "kind": "arxiv",
    "version": 3
  }
}