Pith Number

pith:BJBYKU6D

pith:2010:BJBYKU6DFFP7V55QHPTKHYIWLQ

not attested not anchored not stored refs pending

Left-orderable fundamental groups and Dehn surgery

Adam Clay, Liam Watson

arxiv:1009.4176 v2 · 2010-09-21 · 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{BJBYKU6DFFP7V55QHPTKHYIWLQ}

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	2026-05-18T04:36:32.957741Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0a438553c3295ffaf7b03be6a3e1165c2e4e4954edad64107ca9bedf93c1b195

Aliases

arxiv: 1009.4176 · arxiv_version: 1009.4176v2 · doi: 10.48550/arxiv.1009.4176 · pith_short_12: BJBYKU6DFFP7 · pith_short_16: BJBYKU6DFFP7V55Q · pith_short_8: BJBYKU6D

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/BJBYKU6DFFP7V55QHPTKHYIWLQ \
  | 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: 0a438553c3295ffaf7b03be6a3e1165c2e4e4954edad64107ca9bedf93c1b195

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "13b4467abd1b1d0417a35ed697c1cd13ecda8fb48136ecd6ab5d81b53e8cc1a9",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2010-09-21T19:28:42Z",
    "title_canon_sha256": "4e49861db02dc6068d3505d81603072833b41f95b3b44c417f13532804cc1a9d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1009.4176",
    "kind": "arxiv",
    "version": 2
  }
}