Pith Number

pith:VAPNTDO4

pith:2026:VAPNTDO4CZ23OUPNOPS4PTSZTY

not attested not anchored not stored refs pending

Ancestries in random $d$-DAGs

Fabian Burghart

arxiv:2606.30475 v1 · 2026-06-29 · math.PR · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VAPNTDO4CZ23OUPNOPS4PTSZTY}

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	2026-06-30T02:18:16.897446Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a81ed98ddc1675b751ed73e5c7ce599e1706851a2910f9fa368c6edc30c237be

Aliases

arxiv: 2606.30475 · arxiv_version: 2606.30475v1 · doi: 10.48550/arxiv.2606.30475 · pith_short_12: VAPNTDO4CZ23 · pith_short_16: VAPNTDO4CZ23OUPN · pith_short_8: VAPNTDO4

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/VAPNTDO4CZ23OUPNOPS4PTSZTY \
  | 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: a81ed98ddc1675b751ed73e5c7ce599e1706851a2910f9fa368c6edc30c237be

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4c5efe21db54a8e401108ea13e6c293cd9f25ea91cdb545014f4f5d57a17947c",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2026-06-29T15:35:46Z",
    "title_canon_sha256": "5bc7212b930b3039a3da851d89f7486d360204440b9a5d180cd46b60b0417cb2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.30475",
    "kind": "arxiv",
    "version": 1
  }
}