Pith Number

pith:6NNTH3GS

pith:2015:6NNTH3GSM5OKMCWW6VYFQJBXES

not attested not anchored not stored refs pending

A characterization of relatively hyperbolic groups via bounded cohomology

Federico Franceschini

arxiv:1505.04465 v2 · 2015-05-17 · math.GR · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{6NNTH3GSM5OKMCWW6VYFQJBXES}

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	2026-05-18T01:00:10.272961Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f35b33ecd2675ca60ad6f57058243724bab5615ea56cacb7a72e4ed9fa6ad6e9

Aliases

arxiv: 1505.04465 · arxiv_version: 1505.04465v2 · doi: 10.48550/arxiv.1505.04465 · pith_short_12: 6NNTH3GSM5OK · pith_short_16: 6NNTH3GSM5OKMCWW · pith_short_8: 6NNTH3GS

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/6NNTH3GSM5OKMCWW6VYFQJBXES \
  | 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: f35b33ecd2675ca60ad6f57058243724bab5615ea56cacb7a72e4ed9fa6ad6e9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "77f3ab433b3b809c7d5cbd0cfc8150f62cfa224f089c215ef3458fed1ab5d459",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2015-05-17T21:47:34Z",
    "title_canon_sha256": "96187927157dfdede58f62d2da3d7f6579b4a82d2f7fcf4b68397041a3bfac22"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1505.04465",
    "kind": "arxiv",
    "version": 2
  }
}