BE-857: atlas: take validated scalars as math operands

[indietyp]

🌟 What is the purpose of this PR?

Make the atlas math functions take validated scalars as operands. Today they take raw floats and validate inside. A caller that already holds a validated value pays the check again, while a caller that does not can pass a negative repulsion strength or a non-finite exponent, and an inverse of zero has no way to say no. Configuration scalars deserialize as raw floats, and the check runs downstream, where a bad document fails late.

For review, the properties this stands on:

• An operand's precondition is its type, such as a non-negative strength or a finite exponent. A function whose result can leave its domain returns an option or a derivation, never a raw value that might be out of range.
• A derivation carries its target domain through the arithmetic and validates once, at its destination. Its typed operators pick the result domain from the scalar operator's output.
• Narrowing from f64 to f32 rounds in the direction the caller names.

🔍 What does this change?

• math/scalar/: the validated scalar family and the operators between them.
• math/derivation/: the derivation type and its exit at the destination domain.
• math/ (kernel, affinity, similarity, bounds, transform, vec2, dvec2, kdtree): operands converted from raw floats to the scalar that states their precondition.
• Configuration: scalars such as a base-2 exponent or a ratio above one deserialize through their validating types, so the parser refuses an invalid document.
• Buffers that zero a block take an allocator.
• Consumers in salt/projector and cli/tui/render follow the signatures.

⚠️ Breaking Changes & Known Issues

• The parser refuses a configuration document with an out-of-domain scalar, where the check used to run at first use. A document that loaded before and failed later now fails at load.

❓ How to test this?

1. cargo nextest run -p hash-graph-atlas --all-features math:: runs the scalar, derivation and kernel tests.
2. Feed a fit configuration with a ratio of 1.0 in a field that wants a ratio above one and see the parser refuse it.

Pre-Merge Checklist 🚀

🚢 Has this modified a publishable library?

This PR:

• does not modify any publishable blocks or libraries, or modifications do not need publishing

📜 Does this require a change to the docs?

The changes in this PR:

• are internal and do not require a docs change

🕸️ Does this require a change to the Turbo Graph?

The changes in this PR:

• do not affect the execution graph

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[codecov]

Codecov Report

❌ Patch coverage is 86.64850% with 98 lines in your changes missing coverage. Please review.
✅ Project coverage is 74.70%. Comparing base (5e18067) to head (4e692d0).

Files with missing lines	Patch %	Lines
...ibs/@local/graph/atlas/src/math/scalar/log2/mod.rs	64.28%	15 Missing ⚠️
...al/graph/atlas/src/math/scalar/non_negative/mod.rs	28.57%	15 Missing ⚠️
...raph/atlas/src/math/scalar/greater_than_one/mod.rs	0.00%	14 Missing ⚠️
...s/@local/graph/atlas/src/math/derivation/domain.rs	80.95%	12 Missing ⚠️
libs/@local/graph/atlas/src/math/derivation/mod.rs	92.59%	12 Missing ⚠️
libs/@local/graph/atlas/src/math/bench.rs	0.00%	8 Missing ⚠️
libs/@local/graph/atlas/src/math/bounds/mod.rs	93.40%	4 Missing and 2 partials ⚠️
...l/graph/atlas/src/math/scalar/unit_fraction/mod.rs	33.33%	6 Missing ⚠️
.../graph/atlas/src/math/scalar/d_non_negative/mod.rs	33.33%	4 Missing ⚠️
libs/@local/graph/atlas/src/cli/tui/render/map.rs	70.00%	2 Missing and 1 partial ⚠️
... and 3 more

Additional details and impacted files

@@                                 Coverage Diff                                 @@
##           bm/be-856-atlas-rewrite-the-crate-documentation    #9707      +/-   ##
===================================================================================
+ Coverage                                            71.73%   74.70%   +2.97%     
===================================================================================
  Files                                                 1181      782     -399     
  Lines                                               118685    86834   -31851     
  Branches                                              5190     3627    -1563     
===================================================================================
- Hits                                                 85136    64869   -20267     
+ Misses                                               32490    21283   -11207     
+ Partials                                              1059      682     -377     

Flag	Coverage Δ
apps.hash-ai-worker-ts	1.99% <ø> (?)
apps.hash-api	?
apps.hash-graph	13.62% <ø> (ø)
local.hash-backend-utils	?
local.hash-isomorphic-utils	?
rust.hash-graph-api	?
rust.hash-graph-atlas	81.21% <86.64%> (+0.13%)	⬆️
rust.hashql-eval	?
rust.hashql-mir	?

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[cursor]

PR Summary

Medium Risk
Touches core UMAP affinity, bounds fitting, and layout numerics with new overflow/refusal paths; invalid config scalars now fail at parse time instead of first use.

Overview
Atlas math now takes validated scalar types (Positive, NonNegative, Finite, and their f64 counterparts) as operands instead of raw floats, so preconditions live in the type system and configuration can reject out-of-domain values at deserialize time.

Affinity and fitting: AffinityCurve stores Positive parameters, accepts NonNegative squared distances and repulsion strength, and routes affinity/gradient math through Derivation so overflows and indeterminate forms fail at validation boundaries. The Levenberg–Marquardt fit accumulates normal equations with derivations and adds overflow tests.

Bounds and TUI: Bounds2 growth (with_minimum_extent, with_aspect_ratio, scaled_about_centre) uses wider f64 corner math and returns Option when corners would leave finite f32 range; serde and zerocopy validation are added. The placement map’s map_bounds propagates that and skips drawing when the viewport is unrepresentable.

Supporting changes: Derivation is split into domain + mod with f32/Finite domain support; FinitePointField gains zeroed_in and copy_from; benchmarks and kernel docs are minor touch-ups.

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[github-actions]

Benchmark results

@rust/hash-graph-benches – Integrations

policy_resolution_large

Function	Value	Mean	Flame graphs
resolve_policies_for_actor	user: empty, selectivity: high, policies: 2002	$$15.1 \mathrm{ms} \pm 178 \mathrm{μs}\left({\color{gray}-3.823 \mathrm{\%}}\right) $$	Flame Graph
resolve_policies_for_actor	user: empty, selectivity: low, policies: 1	$$1.98 \mathrm{ms} \pm 11.2 \mathrm{μs}\left({\color{gray}-0.458 \mathrm{\%}}\right) $$	Flame Graph
resolve_policies_for_actor	user: empty, selectivity: medium, policies: 1002	$$7.01 \mathrm{ms} \pm 54.7 \mathrm{μs}\left({\color{gray}-1.639 \mathrm{\%}}\right) $$	Flame Graph
resolve_policies_for_actor	user: seeded, selectivity: high, policies: 3314	$$24.8 \mathrm{ms} \pm 257 \mathrm{μs}\left({\color{gray}-0.013 \mathrm{\%}}\right) $$	Flame Graph
resolve_policies_for_actor	user: seeded, selectivity: low, policies: 1	$$8.84 \mathrm{ms} \pm 69.1 \mathrm{μs}\left({\color{gray}1.08 \mathrm{\%}}\right) $$	Flame Graph
resolve_policies_for_actor	user: seeded, selectivity: medium, policies: 1527	$$13.8 \mathrm{ms} \pm 136 \mathrm{μs}\left({\color{gray}-0.798 \mathrm{\%}}\right) $$	Flame Graph
resolve_policies_for_actor	user: system, selectivity: high, policies: 2078	$$15.7 \mathrm{ms} \pm 189 \mathrm{μs}\left({\color{gray}-3.055 \mathrm{\%}}\right) $$	Flame Graph
resolve_policies_for_actor	user: system, selectivity: low, policies: 1	$$2.19 \mathrm{ms} \pm 10.3 \mathrm{μs}\left({\color{gray}-0.411 \mathrm{\%}}\right) $$	Flame Graph
resolve_policies_for_actor	user: system, selectivity: medium, policies: 1033	$$7.56 \mathrm{ms} \pm 79.7 \mathrm{μs}\left({\color{gray}-2.755 \mathrm{\%}}\right) $$	Flame Graph

policy_resolution_medium

Function	Value	Mean	Flame graphs
resolve_policies_for_actor	user: empty, selectivity: high, policies: 102	$$2.17 \mathrm{ms} \pm 15.6 \mathrm{μs}\left({\color{gray}-0.681 \mathrm{\%}}\right) $$	Flame Graph
resolve_policies_for_actor	user: empty, selectivity: low, policies: 1	$$1.78 \mathrm{ms} \pm 10.2 \mathrm{μs}\left({\color{gray}-0.437 \mathrm{\%}}\right) $$	Flame Graph
resolve_policies_for_actor	user: empty, selectivity: medium, policies: 52	$$1.99 \mathrm{ms} \pm 14.7 \mathrm{μs}\left({\color{gray}-0.573 \mathrm{\%}}\right) $$	Flame Graph
resolve_policies_for_actor	user: seeded, selectivity: high, policies: 269	$$2.96 \mathrm{ms} \pm 14.1 \mathrm{μs}\left({\color{gray}-2.070 \mathrm{\%}}\right) $$	Flame Graph
resolve_policies_for_actor	user: seeded, selectivity: low, policies: 1	$$2.07 \mathrm{ms} \pm 9.93 \mathrm{μs}\left({\color{gray}-0.628 \mathrm{\%}}\right) $$	Flame Graph
resolve_policies_for_actor	user: seeded, selectivity: medium, policies: 108	$$2.36 \mathrm{ms} \pm 9.77 \mathrm{μs}\left({\color{gray}-3.992 \mathrm{\%}}\right) $$	Flame Graph
resolve_policies_for_actor	user: system, selectivity: high, policies: 133	$$2.53 \mathrm{ms} \pm 18.1 \mathrm{μs}\left({\color{gray}-3.025 \mathrm{\%}}\right) $$	Flame Graph
resolve_policies_for_actor	user: system, selectivity: low, policies: 1	$$2.03 \mathrm{ms} \pm 15.2 \mathrm{μs}\left({\color{gray}0.292 \mathrm{\%}}\right) $$	Flame Graph
resolve_policies_for_actor	user: system, selectivity: medium, policies: 63	$$2.32 \mathrm{ms} \pm 9.43 \mathrm{μs}\left({\color{gray}-4.048 \mathrm{\%}}\right) $$	Flame Graph

policy_resolution_none

Function	Value	Mean	Flame graphs
resolve_policies_for_actor	user: empty, selectivity: high, policies: 2	$$1.60 \mathrm{ms} \pm 7.23 \mathrm{μs}\left({\color{gray}0.514 \mathrm{\%}}\right) $$	Flame Graph
resolve_policies_for_actor	user: empty, selectivity: low, policies: 1	$$1.66 \mathrm{ms} \pm 26.6 \mathrm{μs}\left({\color{red}6.12 \mathrm{\%}}\right) $$	Flame Graph
resolve_policies_for_actor	user: empty, selectivity: medium, policies: 2	$$1.64 \mathrm{ms} \pm 5.30 \mathrm{μs}\left({\color{gray}-0.708 \mathrm{\%}}\right) $$	Flame Graph
resolve_policies_for_actor	user: system, selectivity: high, policies: 8	$$1.89 \mathrm{ms} \pm 33.9 \mathrm{μs}\left({\color{gray}4.16 \mathrm{\%}}\right) $$	Flame Graph
resolve_policies_for_actor	user: system, selectivity: low, policies: 1	$$1.74 \mathrm{ms} \pm 19.4 \mathrm{μs}\left({\color{gray}3.10 \mathrm{\%}}\right) $$	Flame Graph
resolve_policies_for_actor	user: system, selectivity: medium, policies: 3	$$1.93 \mathrm{ms} \pm 21.2 \mathrm{μs}\left({\color{gray}2.43 \mathrm{\%}}\right) $$	Flame Graph

policy_resolution_small

Function	Value	Mean	Flame graphs
resolve_policies_for_actor	user: empty, selectivity: high, policies: 52	$$1.82 \mathrm{ms} \pm 8.94 \mathrm{μs}\left({\color{gray}1.36 \mathrm{\%}}\right) $$	Flame Graph
resolve_policies_for_actor	user: empty, selectivity: low, policies: 1	$$1.65 \mathrm{ms} \pm 8.58 \mathrm{μs}\left({\color{gray}0.922 \mathrm{\%}}\right) $$	Flame Graph
resolve_policies_for_actor	user: empty, selectivity: medium, policies: 26	$$1.75 \mathrm{ms} \pm 8.20 \mathrm{μs}\left({\color{gray}-1.371 \mathrm{\%}}\right) $$	Flame Graph
resolve_policies_for_actor	user: seeded, selectivity: high, policies: 94	$$2.02 \mathrm{ms} \pm 16.5 \mathrm{μs}\left({\color{gray}-0.372 \mathrm{\%}}\right) $$	Flame Graph
resolve_policies_for_actor	user: seeded, selectivity: low, policies: 1	$$1.82 \mathrm{ms} \pm 8.51 \mathrm{μs}\left({\color{gray}-0.154 \mathrm{\%}}\right) $$	Flame Graph
resolve_policies_for_actor	user: seeded, selectivity: medium, policies: 27	$$1.98 \mathrm{ms} \pm 11.9 \mathrm{μs}\left({\color{gray}0.832 \mathrm{\%}}\right) $$	Flame Graph
resolve_policies_for_actor	user: system, selectivity: high, policies: 66	$$1.98 \mathrm{ms} \pm 8.94 \mathrm{μs}\left({\color{gray}0.843 \mathrm{\%}}\right) $$	Flame Graph
resolve_policies_for_actor	user: system, selectivity: low, policies: 1	$$1.83 \mathrm{ms} \pm 12.1 \mathrm{μs}\left({\color{gray}1.00 \mathrm{\%}}\right) $$	Flame Graph
resolve_policies_for_actor	user: system, selectivity: medium, policies: 29	$$2.01 \mathrm{ms} \pm 19.6 \mathrm{μs}\left({\color{gray}2.67 \mathrm{\%}}\right) $$	Flame Graph

read_scaling_complete

Function	Value	Mean	Flame graphs
entity_by_id;one_depth	1 entities	$$18.9 \mathrm{ms} \pm 80.5 \mathrm{μs}\left({\color{gray}-2.661 \mathrm{\%}}\right) $$	Flame Graph
entity_by_id;one_depth	10 entities	$$38.7 \mathrm{ms} \pm 199 \mathrm{μs}\left({\color{gray}-0.226 \mathrm{\%}}\right) $$	Flame Graph
entity_by_id;one_depth	25 entities	$$20.8 \mathrm{ms} \pm 141 \mathrm{μs}\left({\color{gray}-1.841 \mathrm{\%}}\right) $$	Flame Graph
entity_by_id;one_depth	5 entities	$$23.1 \mathrm{ms} \pm 274 \mathrm{μs}\left({\color{gray}3.17 \mathrm{\%}}\right) $$	Flame Graph
entity_by_id;one_depth	50 entities	$$24.0 \mathrm{ms} \pm 271 \mathrm{μs}\left({\color{gray}-1.107 \mathrm{\%}}\right) $$	Flame Graph
entity_by_id;two_depth	1 entities	$$19.6 \mathrm{ms} \pm 74.7 \mathrm{μs}\left({\color{gray}-2.237 \mathrm{\%}}\right) $$	Flame Graph
entity_by_id;two_depth	10 entities	$$217 \mathrm{ms} \pm 951 \mathrm{μs}\left({\color{gray}-0.620 \mathrm{\%}}\right) $$	Flame Graph
entity_by_id;two_depth	25 entities	$$48.9 \mathrm{ms} \pm 253 \mathrm{μs}\left({\color{gray}-0.128 \mathrm{\%}}\right) $$	Flame Graph
entity_by_id;two_depth	5 entities	$$40.8 \mathrm{ms} \pm 260 \mathrm{μs}\left({\color{gray}-0.914 \mathrm{\%}}\right) $$	Flame Graph
entity_by_id;two_depth	50 entities	$$145 \mathrm{ms} \pm 494 \mathrm{μs}\left({\color{gray}-1.242 \mathrm{\%}}\right) $$	Flame Graph
entity_by_id;zero_depth	1 entities	$$6.23 \mathrm{ms} \pm 61.6 \mathrm{μs}\left({\color{gray}0.790 \mathrm{\%}}\right) $$	Flame Graph
entity_by_id;zero_depth	10 entities	$$6.24 \mathrm{ms} \pm 28.5 \mathrm{μs}\left({\color{gray}-0.062 \mathrm{\%}}\right) $$	Flame Graph
entity_by_id;zero_depth	25 entities	$$6.35 \mathrm{ms} \pm 36.0 \mathrm{μs}\left({\color{gray}1.03 \mathrm{\%}}\right) $$	Flame Graph
entity_by_id;zero_depth	5 entities	$$6.28 \mathrm{ms} \pm 50.5 \mathrm{μs}\left({\color{gray}-1.171 \mathrm{\%}}\right) $$	Flame Graph
entity_by_id;zero_depth	50 entities	$$6.33 \mathrm{ms} \pm 30.2 \mathrm{μs}\left({\color{gray}-2.245 \mathrm{\%}}\right) $$	Flame Graph

read_scaling_linkless

Function	Value	Mean	Flame graphs
entity_by_id	1 entities	$$6.40 \mathrm{ms} \pm 59.5 \mathrm{μs}\left({\color{gray}3.17 \mathrm{\%}}\right) $$	Flame Graph
entity_by_id	10 entities	$$6.23 \mathrm{ms} \pm 47.0 \mathrm{μs}\left({\color{gray}0.970 \mathrm{\%}}\right) $$	Flame Graph
entity_by_id	100 entities	$$6.26 \mathrm{ms} \pm 65.1 \mathrm{μs}\left({\color{gray}0.947 \mathrm{\%}}\right) $$	Flame Graph
entity_by_id	1000 entities	$$6.22 \mathrm{ms} \pm 32.0 \mathrm{μs}\left({\color{gray}-0.242 \mathrm{\%}}\right) $$	Flame Graph
entity_by_id	10000 entities	$$6.53 \mathrm{ms} \pm 89.4 \mathrm{μs}\left({\color{gray}1.74 \mathrm{\%}}\right) $$	Flame Graph

representative_read_entity

Function	Value	Mean	Flame graphs
entity_by_id	entity type ID: https://blockprotocol.org/@alice/types/entity-type/block/v/1	$$6.59 \mathrm{ms} \pm 76.4 \mathrm{μs}\left({\color{gray}1.53 \mathrm{\%}}\right) $$	Flame Graph
entity_by_id	entity type ID: https://blockprotocol.org/@alice/types/entity-type/book/v/1	$$6.54 \mathrm{ms} \pm 70.7 \mathrm{μs}\left({\color{gray}1.14 \mathrm{\%}}\right) $$	Flame Graph
entity_by_id	entity type ID: https://blockprotocol.org/@alice/types/entity-type/building/v/1	$$6.46 \mathrm{ms} \pm 29.5 \mathrm{μs}\left({\color{gray}0.408 \mathrm{\%}}\right) $$	Flame Graph
entity_by_id	entity type ID: https://blockprotocol.org/@alice/types/entity-type/organization/v/1	$$6.63 \mathrm{ms} \pm 73.1 \mathrm{μs}\left({\color{gray}2.88 \mathrm{\%}}\right) $$	Flame Graph
entity_by_id	entity type ID: https://blockprotocol.org/@alice/types/entity-type/page/v/2	$$6.44 \mathrm{ms} \pm 29.2 \mathrm{μs}\left({\color{gray}-3.335 \mathrm{\%}}\right) $$	Flame Graph
entity_by_id	entity type ID: https://blockprotocol.org/@alice/types/entity-type/person/v/1	$$6.59 \mathrm{ms} \pm 85.6 \mathrm{μs}\left({\color{gray}0.418 \mathrm{\%}}\right) $$	Flame Graph
entity_by_id	entity type ID: https://blockprotocol.org/@alice/types/entity-type/playlist/v/1	$$6.52 \mathrm{ms} \pm 36.4 \mathrm{μs}\left({\color{gray}1.87 \mathrm{\%}}\right) $$	Flame Graph
entity_by_id	entity type ID: https://blockprotocol.org/@alice/types/entity-type/song/v/1	$$6.53 \mathrm{ms} \pm 33.4 \mathrm{μs}\left({\color{gray}1.05 \mathrm{\%}}\right) $$	Flame Graph
entity_by_id	entity type ID: https://blockprotocol.org/@alice/types/entity-type/uk-address/v/1	$$6.72 \mathrm{ms} \pm 97.4 \mathrm{μs}\left({\color{gray}3.11 \mathrm{\%}}\right) $$	Flame Graph

representative_read_entity_type

Function	Value	Mean	Flame graphs
get_entity_type_by_id	Account ID: bf5a9ef5-dc3b-43cf-a291-6210c0321eba	$$4.83 \mathrm{ms} \pm 39.4 \mathrm{μs}\left({\color{gray}1.23 \mathrm{\%}}\right) $$	Flame Graph

representative_read_multiple_entities

Function	Value	Mean	Flame graphs
entity_by_property	traversal_paths=0	0	$$34.9 \mathrm{ms} \pm 343 \mathrm{μs}\left({\color{gray}0.714 \mathrm{\%}}\right) $$
entity_by_property	traversal_paths=255	1,resolve_depths=inherit:1;values:255;properties:255;links:127;link_dests:126;type:true	$$65.0 \mathrm{ms} \pm 408 \mathrm{μs}\left({\color{gray}1.91 \mathrm{\%}}\right) $$
entity_by_property	traversal_paths=2	1,resolve_depths=inherit:0;values:0;properties:0;links:0;link_dests:0;type:false	$$39.1 \mathrm{ms} \pm 335 \mathrm{μs}\left({\color{red}6.71 \mathrm{\%}}\right) $$
entity_by_property	traversal_paths=2	1,resolve_depths=inherit:0;values:0;properties:0;links:1;link_dests:0;type:true	$$44.9 \mathrm{ms} \pm 444 \mathrm{μs}\left({\color{gray}4.76 \mathrm{\%}}\right) $$
entity_by_property	traversal_paths=2	1,resolve_depths=inherit:0;values:0;properties:2;links:1;link_dests:0;type:true	$$48.7 \mathrm{ms} \pm 277 \mathrm{μs}\left({\color{gray}0.708 \mathrm{\%}}\right) $$
entity_by_property	traversal_paths=2	1,resolve_depths=inherit:0;values:2;properties:2;links:1;link_dests:0;type:true	$$52.9 \mathrm{ms} \pm 356 \mathrm{μs}\left({\color{gray}2.05 \mathrm{\%}}\right) $$
link_by_source_by_property	traversal_paths=0	0	$$27.2 \mathrm{ms} \pm 165 \mathrm{μs}\left({\color{red}9.03 \mathrm{\%}}\right) $$
link_by_source_by_property	traversal_paths=255	1,resolve_depths=inherit:1;values:255;properties:255;links:127;link_dests:126;type:true	$$44.3 \mathrm{ms} \pm 319 \mathrm{μs}\left({\color{red}7.80 \mathrm{\%}}\right) $$
link_by_source_by_property	traversal_paths=2	1,resolve_depths=inherit:0;values:0;properties:0;links:0;link_dests:0;type:false	$$31.2 \mathrm{ms} \pm 234 \mathrm{μs}\left({\color{red}5.67 \mathrm{\%}}\right) $$
link_by_source_by_property	traversal_paths=2	1,resolve_depths=inherit:0;values:0;properties:0;links:1;link_dests:0;type:true	$$35.9 \mathrm{ms} \pm 225 \mathrm{μs}\left({\color{gray}2.69 \mathrm{\%}}\right) $$
link_by_source_by_property	traversal_paths=2	1,resolve_depths=inherit:0;values:0;properties:2;links:1;link_dests:0;type:true	$$36.1 \mathrm{ms} \pm 260 \mathrm{μs}\left({\color{gray}2.41 \mathrm{\%}}\right) $$
link_by_source_by_property	traversal_paths=2	1,resolve_depths=inherit:0;values:2;properties:2;links:1;link_dests:0;type:true	$$34.4 \mathrm{ms} \pm 281 \mathrm{μs}\left({\color{lightgreen}-7.006 \mathrm{\%}}\right) $$

scenarios

Function	Value	Mean	Flame graphs
full_test	query-limited	$$68.9 \mathrm{ms} \pm 349 \mathrm{μs}\left({\color{gray}2.08 \mathrm{\%}}\right) $$	Flame Graph
full_test	query-unlimited	$$73.9 \mathrm{ms} \pm 321 \mathrm{μs}\left({\color{gray}-0.559 \mathrm{\%}}\right) $$	Flame Graph
linked_queries	query-limited	$$9.99 \mathrm{ms} \pm 49.4 \mathrm{μs}\left({\color{lightgreen}-20.582 \mathrm{\%}}\right) $$	Flame Graph
linked_queries	query-unlimited	$$301 \mathrm{ms} \pm 821 \mathrm{μs}\left({\color{gray}-1.576 \mathrm{\%}}\right) $$	Flame Graph