Pith Number

pith:UN3WZR45

pith:2014:UN3WZR45GL65G6LVFXSVUBFWBZ

not attested not anchored not stored refs pending

Constructing thin subgroups commensurable with the figure-eight knot group

Darren Long, Samuel A. Ballas

arxiv:1410.8157 v2 · 2014-10-29 · math.GT

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{UN3WZR45GL65G6LVFXSVUBFWBZ}

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	2026-05-18T01:18:52.869938Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a3776cc79d32fdd379752de55a04b60e58632e4b56264ab7cf70f35870e27cc2

Aliases

arxiv: 1410.8157 · arxiv_version: 1410.8157v2 · doi: 10.48550/arxiv.1410.8157 · pith_short_12: UN3WZR45GL65 · pith_short_16: UN3WZR45GL65G6LV · pith_short_8: UN3WZR45

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/UN3WZR45GL65G6LVFXSVUBFWBZ \
  | 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: a3776cc79d32fdd379752de55a04b60e58632e4b56264ab7cf70f35870e27cc2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "55490abb57040ce081e16dfe342a3601b7746bb232d2752dc8b85beaaa3e67bc",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2014-10-29T20:42:26Z",
    "title_canon_sha256": "01c69dad402c6a5ded3319858364905307ec406af6ef6fff6cc5105aa7dcd704"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1410.8157",
    "kind": "arxiv",
    "version": 2
  }
}