Pith Number

pith:PHXRKUEP

pith:2026:PHXRKUEPR7T4SX4HXS2NVH3NB4

not attested not anchored not stored refs pending

Applications of Almost Stationarity I: Quantitative Growth of Injectivity Radius and St\"{u}ck-Zimmer Theorem

Ilya Gekhtman, Omri Solan, Simon Machado, Yuval Yifrach

arxiv:2608.01382 v1 · 2026-08-02 · 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{PHXRKUEPR7T4SX4HXS2NVH3NB4}

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	2026-08-04T02:04:55.200396Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

79ef15508f8fe7c95f87bcb4da9f6d0f3c1d1a4bcc2ab677b0e7140e5be65e08

Aliases

arxiv: 2608.01382 · arxiv_version: 2608.01382v1 · doi: 10.48550/arxiv.2608.01382 · pith_short_12: PHXRKUEPR7T4 · pith_short_16: PHXRKUEPR7T4SX4H · pith_short_8: PHXRKUEP

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/PHXRKUEPR7T4SX4HXS2NVH3NB4 \
  | 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: 79ef15508f8fe7c95f87bcb4da9f6d0f3c1d1a4bcc2ab677b0e7140e5be65e08

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4711a076c6d23ae119ea1207d67478e06d8ab7c9fc5a64eb184d91d712220eec",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2026-08-02T17:04:23Z",
    "title_canon_sha256": "0c8a3c9582a152adb2c9dc79da7fd991fc65f0848b4a50b2f23117d31ce650cb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2608.01382",
    "kind": "arxiv",
    "version": 1
  }
}