Pith Number

pith:KLGUQ7W7

pith:2011:KLGUQ7W7AKJQCVM6AL3PKHZCBI

not attested not anchored not stored refs pending

On L-spaces and left-orderable fundamental groups

Cameron McA. Gordon, Liam Watson, Steven Boyer

arxiv:1107.5016 v1 · 2011-07-25 · 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{KLGUQ7W7AKJQCVM6AL3PKHZCBI}

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	2026-05-18T04:16:54.012957Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

52cd487edf029301559e02f6f51f220a2b1fbcc489c70aa3b31250c81f616dbc

Aliases

arxiv: 1107.5016 · arxiv_version: 1107.5016v1 · doi: 10.48550/arxiv.1107.5016 · pith_short_12: KLGUQ7W7AKJQ · pith_short_16: KLGUQ7W7AKJQCVM6 · pith_short_8: KLGUQ7W7

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/KLGUQ7W7AKJQCVM6AL3PKHZCBI \
  | 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: 52cd487edf029301559e02f6f51f220a2b1fbcc489c70aa3b31250c81f616dbc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "09ad0f450ccfb212a49d393b89de890453fe032c78f22f6399d876e6aea37c62",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2011-07-25T18:44:06Z",
    "title_canon_sha256": "dd55bde252cd39281c66176c61da13872979769a117a687771e0a32ec5d70cbd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1107.5016",
    "kind": "arxiv",
    "version": 1
  }
}