Pith Number

pith:5O24AHIQ

pith:2026:5O24AHIQT27K6TJYYDVSOZ3GVV

not attested not anchored not stored refs pending

Coarse embeddings of products of trees as quasi-isometry invariants

Alessandro Sisto, Mark Hagen

arxiv:2607.08356 v1 · 2026-07-09 · math.GT · math.GR · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{5O24AHIQT27K6TJYYDVSOZ3GVV}

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	2026-07-10T01:19:47.985285Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ebb5c01d109ebeaf4d38c0eb276766ad6e18c5cfb69d04a2d5a8b17bfd34a2db

Aliases

arxiv: 2607.08356 · arxiv_version: 2607.08356v1 · doi: 10.48550/arxiv.2607.08356 · pith_short_12: 5O24AHIQT27K · pith_short_16: 5O24AHIQT27K6TJY · pith_short_8: 5O24AHIQ

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/5O24AHIQT27K6TJYYDVSOZ3GVV \
  | 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: ebb5c01d109ebeaf4d38c0eb276766ad6e18c5cfb69d04a2d5a8b17bfd34a2db

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9f697dd0f309054d9007f59db7c2cbdd5d11588aa4151678b254affc611667db",
    "cross_cats_sorted": [
      "math.GR",
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2026-07-09T11:07:59Z",
    "title_canon_sha256": "72facaf04e5b7da33c24ddf05974dd64e3e63368d9ad23cb9ed2cf338b7b9943"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.08356",
    "kind": "arxiv",
    "version": 1
  }
}