Pith Number

pith:3GWSV3PR

pith:2010:3GWSV3PRFFI2GOJRMS3NU4LTF4

not attested not anchored not stored refs pending

A remark on Alexander polynomial criterion for bi-orderability of fibered 3-manifold groups

Tetsuya Ito

arxiv:1012.0635 v1 · 2010-12-03 · 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{3GWSV3PRFFI2GOJRMS3NU4LTF4}

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	2026-05-18T02:28:29.649311Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d9ad2aedf12951a3393164b6da71732f28568f32012d32113fc3dff4aacc96f1

Aliases

arxiv: 1012.0635 · arxiv_version: 1012.0635v1 · doi: 10.48550/arxiv.1012.0635 · pith_short_12: 3GWSV3PRFFI2 · pith_short_16: 3GWSV3PRFFI2GOJR · pith_short_8: 3GWSV3PR

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/3GWSV3PRFFI2GOJRMS3NU4LTF4 \
  | 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: d9ad2aedf12951a3393164b6da71732f28568f32012d32113fc3dff4aacc96f1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "24cfd9288ce1e50e8ae96b7b2105e931fafbc6abec3f6c1b23ee727072594413",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2010-12-03T04:06:54Z",
    "title_canon_sha256": "195bd6fa69a9c0509c4a03aa365098f75e69246715fbcdd0abe12229da38f47f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.0635",
    "kind": "arxiv",
    "version": 1
  }
}