A representation principle · measured · open source
BH is a representation model where multiple — possibly contradictory — interpretations share one immutable substrate and stay queryable, without duplicating the data and without forcing them into a single truth.

The heart, in one line: don't duplicate the world every time someone disagrees with it. Our sweep identified this — rival interpretations kept as first-class entities — as the property that best distinguishes BH from the approaches evaluated; we give it a working name: FCIR. Provisional conclusion: the universal-paradigm claim was not confirmed, and FCIR already exists in RDF named graphs and standoff annotation — judge it as a synthesis, not an invention.

DOI 10.5281/zenodo.20821058

FCIR — the model in one picture

Same model, as text
   Interp A (alice):  sky   cat   road     coexist · co-registered · first-class
   Interp B (bob):    sky   cat   road
   Interp C (carol):  sky   DOG   road     (disagree at e2 — both kept)
                       |     |     |
   substrate:          e1    e2    e3       immutable · stored once
                             |
       read-time adjudication (OPTIONAL · not stored):
          one lens   ·   majority -> "cat"   ·   keep the disagreement

What makes it different — and what doesn't

Storing a substrate once and reading it selectively is already mature SOTA (DICOM, COG, lakeFS, S-LoRA…) — BH does not claim that. A 20-domain sweep found the FCIR still under-explored: the same model held across four very different prototypes —

instancedomainthe same model, instantiated
bhannorival annotationsK labelings coexist, adjudication optional — the purest
bhmemagent memoryconflicting versions over one history
bhckptmodel checkpointsalternative readings of one shared base
bhtracetracescompeting lenses over one span tree

Where it helps most (honestly): preserving annotator disagreement in ML — keeping every reading first-class instead of collapsing to one gold label ("learning from disagreement"). See the Conclusion.

The Principle (FCIR) →
What FCIR is, the falsifiable test, and the honest confrontation with Git, RDF named graphs, CRDTs, bitemporal, standoff, event sourcing.
The Algebra →
The formal model — operators and laws; FCIR as ⊕ ⊥ α (coexistence decoupled from adjudication).
Conclusion (provisional) →
The universal-paradigm hypothesis was not confirmed; what survived; the response to external critique.
The Study (measured) →
9 angles tested, declared method, honest baselines, public self-corrections.
Code on GitHub →
Four .bh prototypes (illustrations, not competitors), the sweep, and how to reproduce everything.
Don't duplicate the world every time someone disagrees with it.
Cite this work
Carvalho, Márcio M. (2026). Hierarchical Bits: A Structural Envelope for Orchestrating Representations — Method, Measurements and Boundaries (published as a technical note on Zenodo). https://doi.org/10.5281/zenodo.20821058.DOI: 10.5281/zenodo.20821058
Hierarchical Bits · © 2025–2026 Márcio M. Carvalho · code under Apache-2.0, docs under CC BY 4.0 · repository