Pith Number

pith:6KDXELOW

pith:2011:6KDXELOWAFQGJZPKXJCFH5BYJP

not attested not anchored not stored refs pending

Harmonic models and spanning forests of residually finite groups

Hanfeng Li, Lewis Bowen

arxiv:1108.4192 v1 · 2011-08-21 · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{6KDXELOWAFQGJZPKXJCFH5BYJP}

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	2026-05-18T04:14:55.972701Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f287722dd6016064e5eaba4453f4384bf2de3269f97f8adbfa09770355adfe6d

Aliases

arxiv: 1108.4192 · arxiv_version: 1108.4192v1 · doi: 10.48550/arxiv.1108.4192 · pith_short_12: 6KDXELOWAFQG · pith_short_16: 6KDXELOWAFQGJZPK · pith_short_8: 6KDXELOW

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/6KDXELOWAFQGJZPKXJCFH5BYJP \
  | 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: f287722dd6016064e5eaba4453f4384bf2de3269f97f8adbfa09770355adfe6d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c2999847ad41bc648fba50a671b1b12e5e137152140eceb0b38777cfe8ae3162",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2011-08-21T17:46:01Z",
    "title_canon_sha256": "d7e46e60aa782dd39d7a285f5be31a40a33d4b6f9b5f0d439c6201239dfc0940"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1108.4192",
    "kind": "arxiv",
    "version": 1
  }
}