Pith Number

pith:PPEBPXTH

pith:2024:PPEBPXTHXO2FYQBPJCMHZFTDQC

not attested not anchored not stored refs pending

Hopf algebras, Steinberg modules, and the unstable cohomology of $SL_n(\mathbb Z)$ and $GL_n(\mathbb Z)$

Avner Ash, Jeremy Miller, Peter Patzt

arxiv:2404.13776 v1 · 2024-04-21 · math.AT · math.KT · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PPEBPXTHXO2FYQBPJCMHZFTDQC}

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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

2 papers in Pith

The Goncharov Lie coalgebra of a field

A projective resolution of the symplectic Steinberg module

Receipt and verification

First computed	2026-07-05T08:10:36.973869Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7bc817de67bbb45c402f48987c966380bc1c8d241f2797efd820a043a3d3d7a3

Aliases

arxiv: 2404.13776 · arxiv_version: 2404.13776v1 · doi: 10.48550/arxiv.2404.13776 · pith_short_12: PPEBPXTHXO2F · pith_short_16: PPEBPXTHXO2FYQBP · pith_short_8: PPEBPXTH

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/PPEBPXTHXO2FYQBPJCMHZFTDQC \
  | 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: 7bc817de67bbb45c402f48987c966380bc1c8d241f2797efd820a043a3d3d7a3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b2f669571a231798de780f2bb9110e089505131001c7411bbaffcd4e57441d15",
    "cross_cats_sorted": [
      "math.KT",
      "math.NT"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2024-04-21T21:11:56Z",
    "title_canon_sha256": "d8bde1fb0867b19b386dc6f341d5bd86dedfea9bdc2d0f851b0322dab7d5ba22"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2404.13776",
    "kind": "arxiv",
    "version": 1
  }
}