Ahnentafel¶
A genealogical numbering system assigning a proband 1, each person’s father twice their number and mother twice plus one.
Core Idea¶
Pedigree collapse means one ancestor may occupy multiple numbered positions, and the system lists direct ancestors rather than collateral relatives or descendants. Binary arithmetic encodes generation and parental path: doubling appends a paternal step, doubling plus one a maternal step, while parity reveals the sex-coded parental role for every position above the proband. The abstraction is therefore identified by a declared carrier, a transformation or constraint over that carrier, and an invariant that tells an analyst whether the named structure is genuinely present.
Scope of Application¶
Ahnentafel belongs to genealogy and is useful where the analyst can specify the typed genealogy carrier, including objects, relations, parameters, conventions, evidence, boundaries, and comparison targets, then evaluate the proband and identifier 1, generation depth, father and mother recurrence, sex-parity convention, ordering, pedigree-collapse handling, missing or uncertain parents and conversion between number and ancestor path are explicit. The scope is broad within that domain but bounded by the need for the proband and identifier 1, generation depth, father and mother recurrence, sex-parity convention, ordering, pedigree-collapse handling, missing or uncertain parents and conversion between number and ancestor path are explicit. The entry records a descriptive analytical identity; practical use requires the governing domain's evidence, standards, and safety obligations.
Clarity¶
The abstraction clarifies a crowded vocabulary by making the proband and identifier 1, generation depth, father and mother recurrence, sex-parity convention, ordering, pedigree-collapse handling, missing or uncertain parents and conversion between number and ancestor path are explicit the center of the account. A claim should name the carrier, the governing operation or relation, the applicable assumptions, and the recognition test.
Manages Complexity¶
Without the abstraction, an analyst must reason directly over many local details: the carrier roles, admissibility assumptions, competing conventions, derived invariants, boundary cases, and proof or validation obligations specific to Ahnentafel. Ahnentafel compresses them into the roles in the structural signature. That compression permits comparison across instances without erasing the variables that determine validity. It also exposes which details may be varied safely and which are constitutive.
Abstract Reasoning¶
- Identify the carrier. State what the elements, states, objects, or observations are: the typed genealogy carrier, including objects, relations, parameters, conventions, evidence, boundaries, and comparison targets. Reject examples whose alleged carrier belongs to a different problem. 2. Lock the constitutive rule. Express the proband and identifier 1, generation depth, father and mother recurrence, sex-parity convention, ordering, pedigree-collapse handling, missing or uncertain parents and conversion between number and ancestor path are explicit independently of one notation or implementation.
Knowledge Transfer¶
Knowledge transfers strongly among subfields of genealogy because they reuse the typed genealogy carrier, including objects, relations, parameters, conventions, evidence, boundaries, and comparison targets, Binary arithmetic encodes generation and parental path: doubling appends a paternal step, doubling plus one a maternal step, while parity reveals the sex-coded parental role for every position above the proband., and type the carrier, state every parameter and convention in the definition, test that the proband and identifier 1, generation depth, father and mother recurrence, sex-parity convention, ordering, pedigree-collapse handling, missing or uncertain parents and conversion between number and ancestor path are explicit, compare the nearest accepted identity, and report counterexamples, uncertainty, and limiting cases.
Relationships to Other Abstractions¶
Current abstraction Ahnentafel Domain-specific
Parents (1) — more general patterns this builds on
-
Ahnentafel is a kind of Hierarchical Address Prime
The proposed strict upward parent is
prime:hierarchical_address.
Hierarchy paths (4) — routes to 4 parentless roots
- Ahnentafel → Hierarchical Address → Hierarchy → Network → Reservoir-Flux Network → Conservation Laws → Invariance
- Ahnentafel → Hierarchical Address → Hierarchy → Order → Relation
- Ahnentafel → Hierarchical Address → Hierarchy → Order → Set and Membership
- Ahnentafel → Hierarchical Address → Hierarchy → Order → Comparison → Self Checking
Neighborhood in Abstraction Space¶
Ahnentafel sits in a moderately populated region (50th percentile for distinctiveness): it has near-neighbors but no dense thicket of look-alikes.
Family — Inheritance, Lineage & Development (17 abstractions)
Nearest neighbors
- Pedigree collapse — 0.93
- Infinitesimal model — 0.89
- Hard inheritance — 0.88
- Tree (abstract data type) — 0.87
- Helly family — 0.87
Computed from structural-signature embeddings · 2026-09-08