Pith Number

pith:7UZKGMRH

pith:2019:7UZKGMRH5GIXRR4ZVO3E5MVGSH

not attested not anchored not stored refs pending

Borel's stable range for the cohomology of arithmetic groups

Bena Tshishiku

arxiv:1904.04902 v1 · 2019-04-09 · math.GR · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7UZKGMRH5GIXRR4ZVO3E5MVGSH}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more

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

Calculating the second rational cohomology group of the Torelli group

Receipt and verification

First computed	2026-05-17T23:48:57.713613Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fd32a33227e99178c799abb64eb2a691c800037644b02c8beca67c347e7fad48

Aliases

arxiv: 1904.04902 · arxiv_version: 1904.04902v1 · doi: 10.48550/arxiv.1904.04902 · pith_short_12: 7UZKGMRH5GIX · pith_short_16: 7UZKGMRH5GIXRR4Z · pith_short_8: 7UZKGMRH

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/7UZKGMRH5GIXRR4ZVO3E5MVGSH \
  | 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: fd32a33227e99178c799abb64eb2a691c800037644b02c8beca67c347e7fad48

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ba4b9afc33f566bdde42c3c7a9fd3e1568ea081d6487fed9acf2bc25a966cff4",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2019-04-09T20:45:08Z",
    "title_canon_sha256": "27d166edb4003ced153b9523835b2f63a73e248dd877813f0ae47d695ab6cfda"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1904.04902",
    "kind": "arxiv",
    "version": 1
  }
}