Only Nodes Cross: Eating and Being Eaten from Cells to Mycelium

Every living thing eats, and every living thing can be eaten. This manuscript maps eating onto the framework as a translation layer. A companion manuscript separated nodes — counts, which carry no mark of their origin — from arcs, the phasing that is specific to one reader. Read with that separation, eating reduces to one rule: nodes and tension cross a reader’s boundary; arcs are reduced outside it and never cross as food. The rule follows from the reader’s source tag. A foreign arc admitted inside would be read as the reader’s own. So the only things that can happen to it are reduction outside the boundary, which is eating, or entry into the record, which is copying.
Consequences:
• The two operations sort all traffic across a living boundary. Nodes are moved in (eating). Arcs are copied in (infection, gene transfer, sex, endosymbiosis). Viruses, which copy and never eat, sit exactly on the line.
• “Outside” is topological, not spatial. The different ways of eating — autotrophs, osmotrophs, phagotrophs, animals, humans — differ only in where the outside is placed and who holds the key: none; the world; a pocket; a tube; the world again, under control.
• Edibility is a band. Food too unlike the eater cannot be reduced, because the eater has no key. Food too like it passes as the eater’s own.
• Food carries two components. Nodes to write into, and tension to pay for the write. The great nutritional mutualisms divide along exactly this line.
• In fungi and roots the eating surface is the generating sheet. Animals separated eating from growing and move to their food.
The individual findings are established. The rule that connects them, the band, the division of mutualisms, and the ladder of placements are what this manuscript contributes. Predictions are given.

The foundational architecture, geometric intuitions, and motivating philosophy of this framework originated independently with the author prior to and separate from any AI involvement. Subsequent mathematical derivation, connection to established physics literature, computational verification, and error-checking were conducted through extended technical work with AI systems (Anthropic’s Claude and Google’s Gemini). The author directed this process, evaluated and selected among proposed derivations, and takes full responsibility for the accuracy and originality of the final work.