Pith Number

pith:W3IYHORI

pith:2015:W3IYHORI4UEDAMHT4ZTOXAO34A

not attested not anchored not stored refs pending

The $\Sigma$-invariants of Thompson's group $F$ via Morse theory

Matthew C. B. Zaremsky, Stefan Witzel

arxiv:1501.06682 v2 · 2015-01-27 · math.GR · 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{W3IYHORI4UEDAMHT4ZTOXAO34A}

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	2026-05-18T02:17:42.534149Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b6d183ba28e5083030f3e666eb81dbe0251f7ae5f2674b0baff8e9c2904edabc

Aliases

arxiv: 1501.06682 · arxiv_version: 1501.06682v2 · doi: 10.48550/arxiv.1501.06682 · pith_short_12: W3IYHORI4UED · pith_short_16: W3IYHORI4UEDAMHT · pith_short_8: W3IYHORI

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/W3IYHORI4UEDAMHT4ZTOXAO34A \
  | 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: b6d183ba28e5083030f3e666eb81dbe0251f7ae5f2674b0baff8e9c2904edabc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "736fcb48f68c41f6250de74878ad92a87f7e75dd8dc35b3fec0d688d72ce83a7",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2015-01-27T08:11:17Z",
    "title_canon_sha256": "00f7bb680bbe517ad1674c3b7490550059c5946c1a955b04605bd3d524193c48"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1501.06682",
    "kind": "arxiv",
    "version": 2
  }
}