Pith Number

pith:4UMF2MJ4

pith:2025:4UMF2MJ4GGWVTWTNRZMPQI6ERE

not attested not anchored not stored refs pending

Poincar\'{e}-Birkhoff-Witt Theorems in Higher Algebra

Gijs Heuts, Lukas Brantner, Omar Antol\'in-Camarena

arxiv:2501.03116 v2 · 2025-01-06 · math.AT · math.CT · math.RT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4UMF2MJ4GGWVTWTNRZMPQI6ERE}

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.

Cited by

1 paper in Pith

On periodic homotopy and homology equivalences of spaces

Receipt and verification

First computed	2026-07-05T11:53:27.269536Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e5185d313c31ad59da6d8e58f823c489075f997e4516f89be16bd49ab64317c9

Aliases

arxiv: 2501.03116 · arxiv_version: 2501.03116v2 · doi: 10.48550/arxiv.2501.03116 · pith_short_12: 4UMF2MJ4GGWV · pith_short_16: 4UMF2MJ4GGWVTWTN · pith_short_8: 4UMF2MJ4

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/4UMF2MJ4GGWVTWTNRZMPQI6ERE \
  | 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: e5185d313c31ad59da6d8e58f823c489075f997e4516f89be16bd49ab64317c9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2f0d65add8a8328bcb4f16886d08e8aae0f6174b62691e4108cc8f94baf49979",
    "cross_cats_sorted": [
      "math.CT",
      "math.RT"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2025-01-06T16:23:32Z",
    "title_canon_sha256": "f56924bad6983710fae6603d268996069d85e8c6fad67f3d498a5e8c1157f463"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2501.03116",
    "kind": "arxiv",
    "version": 2
  }
}