Pith Number

pith:AFTAPSIJ

pith:2023:AFTAPSIJSVW2GZ2EDV5XV5CEC5

not attested not anchored not stored refs pending

A presentation of symplectic Steinberg modules and cohomology of $\operatorname{Sp}_{2n}(\mathbb{Z})$

Benjamin Br\"uck, Peter Patzt, Robin J. Sroka

arxiv:2306.03180 v1 · 2023-06-05 · math.AT · math.AG · math.GR · math.GT · math.NT

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Add to your LaTeX paper

\usepackage{pith}
\pithnumber{AFTAPSIJSVW2GZ2EDV5XV5CEC5}

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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

A projective resolution of the symplectic Steinberg module

Receipt and verification

First computed	2026-07-05T06:17:54.736630Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

016607c909956da367441d7b7af44417611c0cc249f42a840c5def68bd45e1fe

Aliases

arxiv: 2306.03180 · arxiv_version: 2306.03180v1 · doi: 10.48550/arxiv.2306.03180 · pith_short_12: AFTAPSIJSVW2 · pith_short_16: AFTAPSIJSVW2GZ2E · pith_short_8: AFTAPSIJ

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/AFTAPSIJSVW2GZ2EDV5XV5CEC5 \
  | 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: 016607c909956da367441d7b7af44417611c0cc249f42a840c5def68bd45e1fe

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ee194ff8c122f32b7719e1f6b835b3f5a25435db15530d9c2c55ccd2a284aa0d",
    "cross_cats_sorted": [
      "math.AG",
      "math.GR",
      "math.GT",
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2023-06-05T18:41:18Z",
    "title_canon_sha256": "0c748e08eaeb96c63361c954284f79dc849f837f3f98c197516e921f3a3cefe7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2306.03180",
    "kind": "arxiv",
    "version": 1
  }
}