Pith Number

pith:LV3VAFDO

pith:2015:LV3VAFDOPOPFWUZWQPTEJGN63R

not attested not anchored not stored refs pending

An upper bound for the pseudoisotopy stable range

Oscar Randal-Williams

arxiv:1511.08557 v2 · 2015-11-27 · math.AT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{LV3VAFDOPOPFWUZWQPTEJGN63R}

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	2026-05-18T00:57:38.149960Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5d7750146e7b9e5b533683e64499bedc4fbb375fd4c36daed1396045d9d07c75

Aliases

arxiv: 1511.08557 · arxiv_version: 1511.08557v2 · doi: 10.48550/arxiv.1511.08557 · pith_short_12: LV3VAFDOPOPF · pith_short_16: LV3VAFDOPOPFWUZW · pith_short_8: LV3VAFDO

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/LV3VAFDOPOPFWUZWQPTEJGN63R \
  | 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: 5d7750146e7b9e5b533683e64499bedc4fbb375fd4c36daed1396045d9d07c75

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8ca45bb9d54b0736558d6c76eba19a49f21d61bf268e2113b3f5c2c0742eb809",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2015-11-27T05:11:03Z",
    "title_canon_sha256": "ce91eda4b5ed18d84064289ef58761f8611262f5d7560ba588e93a01ed112600"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1511.08557",
    "kind": "arxiv",
    "version": 2
  }
}