Pith Number

pith:SMQB24NE

pith:2013:SMQB24NEZ54HSXIQU4MDQV5SWU

not attested not anchored not stored refs pending

Growth tightness for groups with contracting elements

Wenyuan Yang

arxiv:1301.5623 v2 · 2013-01-23 · 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{SMQB24NEZ54HSXIQU4MDQV5SWU}

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	2026-05-17T23:53:35.827062Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

93201d71a4cf78795d10a7183857b2b507929476b2ae91de2a6430dc94b6f347

Aliases

arxiv: 1301.5623 · arxiv_version: 1301.5623v2 · doi: 10.48550/arxiv.1301.5623 · pith_short_12: SMQB24NEZ54H · pith_short_16: SMQB24NEZ54HSXIQ · pith_short_8: SMQB24NE

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/SMQB24NEZ54HSXIQU4MDQV5SWU \
  | 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: 93201d71a4cf78795d10a7183857b2b507929476b2ae91de2a6430dc94b6f347

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ae5cb5ace81eb6fa2a63e38a427ec4710745fa4fbc5b060c5572af7c04493232",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2013-01-23T20:33:33Z",
    "title_canon_sha256": "42ec11f1ec8599d130b6cdb5e51607a6e989790db0cb51db18584ee01f5e6ba3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1301.5623",
    "kind": "arxiv",
    "version": 2
  }
}