Pith Number

pith:UH4HKXG3

pith:2018:UH4HKXG3CIP4J3GTTL26LY4OMI

not attested not anchored not stored refs pending

Gaps in scl for Amalgamated Free Products and RAAGs

Nicolaus Heuer

arxiv:1802.01107 v3 · 2018-02-04 · math.GT · 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{UH4HKXG3CIP4J3GTTL26LY4OMI}

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	2026-05-18T00:05:45.914154Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a1f8755cdb121fc4ecd39af5e5e38e6200a139793f2e3771f533405d88f18f0c

Aliases

arxiv: 1802.01107 · arxiv_version: 1802.01107v3 · doi: 10.48550/arxiv.1802.01107 · pith_short_12: UH4HKXG3CIP4 · pith_short_16: UH4HKXG3CIP4J3GT · pith_short_8: UH4HKXG3

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/UH4HKXG3CIP4J3GTTL26LY4OMI \
  | 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: a1f8755cdb121fc4ecd39af5e5e38e6200a139793f2e3771f533405d88f18f0c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2734b49974f58eb95bc9310a9ddedc92100fd2ab1d07fa0fc1e6852f5e92c132",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2018-02-04T10:45:35Z",
    "title_canon_sha256": "5036dc45c19a85de09719984f3cfe7080d2d5463011a83977402eb068615bef6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1802.01107",
    "kind": "arxiv",
    "version": 3
  }
}