Pith Number

pith:2V7AKWIM

pith:2025:2V7AKWIMQS6O2LJPZRREZ4YPR4

not attested not anchored not stored refs pending

Functoriality of the Klein-Williams Invariant and Universality Theory

Ba\c{s}ak K\"u\c{c}\"uk

arxiv:2505.22376 v1 · 2025-05-28 · 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{2V7AKWIMQS6O2LJPZRREZ4YPR4}

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	2026-07-05T11:11:14.096259Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d57e05590c84bced2d2fcc624cf30f8f3275f9b0c011708dc3120a56c92564fe

Aliases

arxiv: 2505.22376 · arxiv_version: 2505.22376v1 · doi: 10.48550/arxiv.2505.22376 · pith_short_12: 2V7AKWIMQS6O · pith_short_16: 2V7AKWIMQS6O2LJP · pith_short_8: 2V7AKWIM

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/2V7AKWIMQS6O2LJPZRREZ4YPR4 \
  | 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: d57e05590c84bced2d2fcc624cf30f8f3275f9b0c011708dc3120a56c92564fe

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a1290266fd154dbe0da17104dbd5bb162158768eb8f6de3223cd6b34da1e4a46",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2025-05-28T14:03:22Z",
    "title_canon_sha256": "1a47785362583585efb46a74193583611bc53d5fde806637e5fff2dc836b632f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2505.22376",
    "kind": "arxiv",
    "version": 1
  }
}