Pith Number

pith:BG55P26O

pith:2016:BG55P26O4FLA5DMGSFBC5JFKSN

not attested not anchored not stored refs pending

Spectral gap of scl in free products

Lvzhou Chen

arxiv:1611.07936 v2 · 2016-11-23 · 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{BG55P26O4FLA5DMGSFBC5JFKSN}

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	2026-05-18T00:39:47.153116Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

09bbd7ebcee1560e8d8691422ea4aa9359bb82bbefa34e13ee1a9d6b3a2602b1

Aliases

arxiv: 1611.07936 · arxiv_version: 1611.07936v2 · doi: 10.48550/arxiv.1611.07936 · pith_short_12: BG55P26O4FLA · pith_short_16: BG55P26O4FLA5DMG · pith_short_8: BG55P26O

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/BG55P26O4FLA5DMGSFBC5JFKSN \
  | 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: 09bbd7ebcee1560e8d8691422ea4aa9359bb82bbefa34e13ee1a9d6b3a2602b1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e492e21bc2d3f6b7fdf169515f2a56422e5213f5483997beff5e9aa5bef291bd",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2016-11-23T19:08:14Z",
    "title_canon_sha256": "0723380c56d5f935ea7f8107f6ed9d6b0fb61e75e26054dcc965dd08039f9dfc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1611.07936",
    "kind": "arxiv",
    "version": 2
  }
}