Pith Number

pith:NBB4MXYI

pith:2009:NBB4MXYITLKTO2UCSCEKAXGRMK

not attested not anchored not stored refs pending

Amenable actions of amalgamated free products of free groups over a cyclic subgroup and generic property

Soyoung Moon

arxiv:0909.2824 v4 · 2009-09-15 · 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{NBB4MXYITLKTO2UCSCEKAXGRMK}

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	2026-05-18T04:38:50.847777Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6843c65f089ad5376a829088a05cd162a8602f6f22aee121935217dd928ec271

Aliases

arxiv: 0909.2824 · arxiv_version: 0909.2824v4 · doi: 10.48550/arxiv.0909.2824 · pith_short_12: NBB4MXYITLKT · pith_short_16: NBB4MXYITLKTO2UC · pith_short_8: NBB4MXYI

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/NBB4MXYITLKTO2UCSCEKAXGRMK \
  | 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: 6843c65f089ad5376a829088a05cd162a8602f6f22aee121935217dd928ec271

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7f2cbca4d26ecc5da1835f39b8e3c215870d917b80faf6f3721ae8f8c19abc1b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2009-09-15T15:24:28Z",
    "title_canon_sha256": "858f91d9e7be5100fef23cc49f15e31dd769bf2f4d6251be5cf4db018b6ab873"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0909.2824",
    "kind": "arxiv",
    "version": 4
  }
}