Pith Number

pith:4Z5WU4UP

pith:2011:4Z5WU4UPMVL2EMPGOVS7WBET3T

not attested not anchored not stored refs pending

Alternating links and left-orderability

Joshua Evan Greene

arxiv:1107.5232 v1 · 2011-07-26 · 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{4Z5WU4UPMVL2EMPGOVS7WBET3T}

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	2026-05-18T04:16:52.683680Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e67b6a728f6557a231e67565fb0493dcc626435ef8fecc12ba0fd9e54aa2c9e8

Aliases

arxiv: 1107.5232 · arxiv_version: 1107.5232v1 · doi: 10.48550/arxiv.1107.5232 · pith_short_12: 4Z5WU4UPMVL2 · pith_short_16: 4Z5WU4UPMVL2EMPG · pith_short_8: 4Z5WU4UP

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/4Z5WU4UPMVL2EMPGOVS7WBET3T \
  | 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: e67b6a728f6557a231e67565fb0493dcc626435ef8fecc12ba0fd9e54aa2c9e8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "54dbcb047883e39a41ef23085790e61cddcdcc32ac004f43ad04ab1dd2cbf2c7",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2011-07-26T15:05:40Z",
    "title_canon_sha256": "ac0fc76601a12066e1c729c2ed06c1104161615d94dcd77f60c1022d87658039"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1107.5232",
    "kind": "arxiv",
    "version": 1
  }
}