Pith Number

pith:VVOFE5W7

pith:2017:VVOFE5W77VVSTGXKIJUHKSTTC2

not attested not anchored not stored refs pending

Beyond Serre's "Trees" in two directions: $\Lambda$--trees and products of trees

Alina Vdovina, Olga Kharlampovich

arxiv:1710.10306 v1 · 2017-10-27 · 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{VVOFE5W77VVSTGXKIJUHKSTTC2}

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	2026-05-18T00:31:49.951247Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ad5c5276dffd6b299aea4268754a731692d79f52d2c7249de4cb49224130c629

Aliases

arxiv: 1710.10306 · arxiv_version: 1710.10306v1 · doi: 10.48550/arxiv.1710.10306 · pith_short_12: VVOFE5W77VVS · pith_short_16: VVOFE5W77VVSTGXK · pith_short_8: VVOFE5W7

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/VVOFE5W77VVSTGXKIJUHKSTTC2 \
  | 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: ad5c5276dffd6b299aea4268754a731692d79f52d2c7249de4cb49224130c629

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a98d3a7dd9e76945b2e9ff0bf1e5a44c72c646fdd82c328783fb65a0d17148a6",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2017-10-27T19:10:12Z",
    "title_canon_sha256": "2303200cdf29cd5f87a1fbea27a5a90fa2a61941ecfe925807170ad583129e85"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1710.10306",
    "kind": "arxiv",
    "version": 1
  }
}