Pith Number

pith:V77ILFUF

pith:2011:V77ILFUF2WQBP5QSHX3JJJ7FUH

not attested not anchored not stored refs pending

Graph manifolds, left-orderability and amalgamation

Adam Clay, Liam Watson, Tye Lidman

arxiv:1106.0486 v1 · 2011-06-02 · 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{V77ILFUF2WQBP5QSHX3JJJ7FUH}

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	2026-05-18T02:41:50.497381Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

affe859685d5a017f6123df694a7e5a1d2c80582fc01b53956230decc5d3c09b

Aliases

arxiv: 1106.0486 · arxiv_version: 1106.0486v1 · doi: 10.48550/arxiv.1106.0486 · pith_short_12: V77ILFUF2WQB · pith_short_16: V77ILFUF2WQBP5QS · pith_short_8: V77ILFUF

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/V77ILFUF2WQBP5QSHX3JJJ7FUH \
  | 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: affe859685d5a017f6123df694a7e5a1d2c80582fc01b53956230decc5d3c09b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9342616a2cbaf677867464a6f7eec356d4e94f7cd054e8646cd85a6430e209a0",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2011-06-02T19:17:13Z",
    "title_canon_sha256": "22bae33f926faebc24094f2b1e43b90ea4710e3d83d36e77f8183756963f1b6f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1106.0486",
    "kind": "arxiv",
    "version": 1
  }
}