Pith Number

pith:5ZAY7S5Z

pith:2016:5ZAY7S5ZDYOZPBTQWXP2JZ6ESW

not attested not anchored not stored refs pending

Multi-type Galton-Watson processes with affinity-dependent selection applied to antibody affinity maturation

Gilles Wainrib, Irene Balelli, Vuk Mili\v{s}i\'c

arxiv:1609.00823 v2 · 2016-09-03 · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{5ZAY7S5ZDYOZPBTQWXP2JZ6ESW}

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	2026-05-18T00:26:51.997213Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ee418fcbb91e1d978670b5dfa4e7c495bb2d1217c853a72024ba8d4551d21076

Aliases

arxiv: 1609.00823 · arxiv_version: 1609.00823v2 · doi: 10.48550/arxiv.1609.00823 · pith_short_12: 5ZAY7S5ZDYOZ · pith_short_16: 5ZAY7S5ZDYOZPBTQ · pith_short_8: 5ZAY7S5Z

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/5ZAY7S5ZDYOZPBTQWXP2JZ6ESW \
  | 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: ee418fcbb91e1d978670b5dfa4e7c495bb2d1217c853a72024ba8d4551d21076

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9a592607363ff55c059a4fffe3de2c77b74240008f6eff8fd3582bd7dc0282b6",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2016-09-03T12:37:53Z",
    "title_canon_sha256": "6d056031e39a0ee34490bc3155cbea5ab56fe92a96d8cf34e32a5030e6ab6c1c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1609.00823",
    "kind": "arxiv",
    "version": 2
  }
}