Pith Number

pith:VYLKUUEP

pith:2018:VYLKUUEPSQJKN6ALG4XZFIFTWX

not attested not anchored not stored refs pending

Bifurcations of the polycycle "tears of the heart": multiple numerical invariants

Nataliya Goncharuk, Yury Kudryashov

arxiv:1808.07459 v3 · 2018-08-22 · 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{VYLKUUEPSQJKN6ALG4XZFIFTWX}

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	2026-05-17T23:57:07.388820Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ae16aa508f9412a6f80b372f92a0b3b5daff5d10aecb5719c5667698e49e4b79

Aliases

arxiv: 1808.07459 · arxiv_version: 1808.07459v3 · doi: 10.48550/arxiv.1808.07459 · pith_short_12: VYLKUUEPSQJK · pith_short_16: VYLKUUEPSQJKN6AL · pith_short_8: VYLKUUEP

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/VYLKUUEPSQJKN6ALG4XZFIFTWX \
  | 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: ae16aa508f9412a6f80b372f92a0b3b5daff5d10aecb5719c5667698e49e4b79

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "773977212037365c3731bbd5ce0b38dc3aecc9240f4887010b78247ca8d4b920",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2018-08-22T17:49:31Z",
    "title_canon_sha256": "8951cb5f47d9416d10b2269f25e2787f04c67cb2e3389a68fb26b6aa4b62d719"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1808.07459",
    "kind": "arxiv",
    "version": 3
  }
}