Invention Disclosure — Aperiodic Structured Nutrient Substrate
Working draft for patent counsel. Not legal advice. Claims below are illustrative skeletons to be reviewed, narrowed, and re-drafted by a registered patent attorney. See §7 (disclosure/priority) — public Zenodo/site/book disclosures have already started a clock.
Inventor: Pablo Nogueira Grossi · G6 LLC, Newark NJ · ORCID 0009-0000-6496-2186 Related: Book 6 · Ch DE-3 — Aperiodic Multiplying Media (live chapter); Book 3 Ch η DNLS; companion criticality paper (Zenodo 10.5281/zenodo.20077205)
1. Field
Structured nutrient substrates, culture/fermentation media, animal feed, and bioreactor packings whose nutrient distribution is spatially ordered by an aperiodic (substitution) rule to control the growth-criticality (persistence/washout) threshold of a biological population.
2. The technical problem
Periodic or homogeneous nutrient substrates give a growth-criticality threshold that is fixed by composition alone and does not scale predictably from bench to plant. Cultures on lean or fluctuating feed drift toward washout with little design margin.
3. The invention (one sentence)
A nutrient substrate in which nutrient-bearing domains are arranged along a spatial axis by a primitive substitution rule of inflation order n (Fibonacci n=2, tribonacci n=3, …), so that the inflation eigenvalue λ_PF becomes a design knob setting the growth-criticality threshold — higher n raises the threshold, conferring robustness against nutrient fluctuation and making bioreactor criticality scale-covariant under inflation.
4. The unexpected effect (non-obviousness anchor)
The self-trapping / persistence threshold rises with n as a difference in regime, not merely magnitude: numerically λ_c(n) ≈ 0.958·Δ_n + 0.107 (r = 0.989), and a tribonacci ordering (η ≈ 1.8393 > φ ≈ 1.6180) holds a localized population together under leaner feed than a Fibonacci ordering of identical bulk composition. This surprising, structure-only advantage — same ingredients, different survival margin — is the §103 non-obviousness anchor.
5. Strongest asset — composition + method-of-use pair
Independent composition claim
1. A structured nutrient substrate for supporting biological growth, comprising a solid or gel matrix defining, along at least one spatial axis, a plurality of nutrient-bearing domains separated by interstitial transport regions, wherein the ordering of the nutrient-bearing domains along said axis follows a primitive substitution rule whose inflation matrix has a Perron–Frobenius eigenvalue λ_PF greater than 1, such that the local nutrient concentration profile along said axis is aperiodic and non-periodic with a characteristic domain-length ratio determined by said substitution rule.
Dependent narrowing:
2. The substrate of claim 1, wherein the substitution rule is the tribonacci rule (a→ab, b→ac, c→a), so that λ_PF = η is the real root of x³ − x² − x − 1 = 0 in (1,2), η ≈ 1.8393.
3. The substrate of claim 1, wherein the substitution rule is an n-bonacci rule with n ≥ 3, so that λ_PF > φ.
4. The substrate of claim 1, wherein the nutrient-bearing domains have characteristic lengths between [X] and [Y] micrometres. (fill from embodiment)
5. The substrate of claim 1, wherein the matrix comprises one of: a cross-linked hydrogel; an extruded feed pellet; an additively-manufactured (3D-printed) scaffold; a cast multilayer.
6. The substrate of claim 1, characterized in that a mid-gap growth mode supported by the substrate has an inverse participation ratio at least K× that of a Fibonacci-ordered substrate of identical bulk composition. (structural-functional limitation carrying the unexpected effect; set K ≈ 3.5–4 from data)
7. The substrate of claim 1, adapted as a scaffold for cultured animal cells for cultivated-meat production.
Independent method-of-use claim
8. A method of culturing a population of organisms, comprising: providing a structured nutrient substrate according to claim 1; inoculating the substrate with the organism; and maintaining culture conditions under which the population preferentially localizes onto the nutrient-bearing domains; wherein the inflation order n of the substitution rule is selected such that the persistence threshold of the population — the critical mean nutrient concentration, or critical patch contrast, below which the population washes out — is above a target value, thereby conferring robustness of the culture against fluctuation in nutrient supply.
Dependent:
9. The method of claim 8, comprising selecting n = 3 rather than n = 2 to raise the persistence threshold.
10. The method of claim 8, wherein the organism is a microbial fermentation strain, a probiotic culture, or a mammalian cell line.
11. The method of claim 8, wherein selecting the inflation order n comprises fabricating the substrate with a physical domain sequence of inflation order n. (ties the selection to a physical act — see §6)
6. Keeping the design-method claims out of §101
A claim reciting "computing λ_PF" or "selecting n to maximize a threshold" as a standalone step is a bare mathematical/mental operation and is abstract under Alice/Mayo. The fix is to never claim the calculation alone — always fold the design choice into a physical transformation with a measurable structural result:
Independent method-of-manufacture claim (§101-safe form of the "design method")
12. A method of manufacturing a structured nutrient substrate, comprising: determining a spatial domain sequence from a primitive substitution rule of inflation order n; and depositing nutrient material to form nutrient-bearing domains physically arranged in said sequence along a spatial axis, by additive manufacturing, extrusion, or layer casting, such that the resulting substrate exhibits an aperiodic nutrient-concentration profile whose characteristic domain-length ratio is set by λ_PF.
Here "determining the sequence" is a limitation on the physical deposition step and the resulting article, not a standalone claim element — the claim rises or falls on making a real object. That is the pattern that survives §101.
Optional QA/QC method (pairs with bomb calorimetry)
13. A method of qualifying a feed or substrate, comprising: measuring a caloric density of the substrate by oxygen-bomb calorimetry; determining, by structural characterization, the inflation order n of the domain sequence; and accepting the substrate when both the caloric density and the inflation order meet specification. (a two-parameter spec: energy + robustness margin)
7. Enablement and priority — action items
- Enablement (§112). The nutrition embodiment is currently predicted, untested. Before a broad filing, add at least one prophetic example and, ideally, one fermentation/culture run showing the threshold shift between n = 2 and n = 3 substrates of equal bulk composition. This converts claim 6's K× limitation from assertion to demonstration.
- Novelty search (§102). Run prior-art on: aperiodic/Fibonacci/quasicrystal structuring of feed, hydrogels, and scaffolds; structured bioreactor packing; patterned nutrient release; cultivated-meat scaffold geometry.
- Priority / disclosure (§102(b) + foreign absolute novelty). The framework has been publicly disclosed (Zenodo preprints, totogt.github.io, Book 6 chapter). US: a one-year grace period runs from the first disclosure of the product embodiment. Most foreign jurisdictions: absolute novelty — prior self-disclosure may already bar. Gather the exact first-publication date of any text describing the physical feed/substrate (not just the abstract math), and treat a provisional filing as time-sensitive.
8. Commercial embodiments (ranked)
- Cultivated-meat scaffolds — structured nutrient/oxygen scaffolds for cell-ag; strong IP frontier; direct adjacency to JBS/Friboi cultivated-meat interests.
- Precision-fermentation feedstocks — robustness against feed fluctuation in industrial fermentation.
- Structured animal-feed pellets — engineered nutrient-release profile with a robustness margin.
- Biofilm carriers / water treatment — aperiodic carrier media for wastewater cultures.