Pith Number

pith:GUCHEKUG

pith:2017:GUCHEKUGQ7WUGTOQPFP37KM6K6

not attested not anchored not stored refs pending

Cup Product in Bounded Cohomology of the Free Group

Nicolaus Heuer

arxiv:1710.03193 v2 · 2017-10-09 · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GUCHEKUGQ7WUGTOQPFP37KM6K6}

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	2026-05-17T23:58:14.853469Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3504722a8687ed434dd0795fbfa99e57835c27c665c74ef18213725cc90836ea

Aliases

arxiv: 1710.03193 · arxiv_version: 1710.03193v2 · doi: 10.48550/arxiv.1710.03193 · pith_short_12: GUCHEKUGQ7WU · pith_short_16: GUCHEKUGQ7WUGTOQ · pith_short_8: GUCHEKUG

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/GUCHEKUGQ7WUGTOQPFP37KM6K6 \
  | 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: 3504722a8687ed434dd0795fbfa99e57835c27c665c74ef18213725cc90836ea

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4410b7db16e79880ff5fb64a87c6fdb172fbc7027d6b8b2d8609d95f3e42e7b5",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2017-10-09T16:58:37Z",
    "title_canon_sha256": "3de6846d38acc5a7b71930297011bbbda9633b99e8febc416d78cabfc73875b2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1710.03193",
    "kind": "arxiv",
    "version": 2
  }
}