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"title": "Three Densities: Proposition 4 — Hysteresis",
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"plaintext": "The original essay (Three Densities) separated platform density into three layers and showed that conversion between them is non-conservative. The state classification there is static: it maps a platform at a single moment. This note introduces time."
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"plaintext": "Proposition 4 (Density Hysteresis)"
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"plaintext": "D3 responds to a decline in D1 with delay."
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"plaintext": "When D1 is high, participants form context-sharing networks: mutual recognition, role awareness, shared reference points. These do not collapse the moment D1 drops. They are cumulative structures."
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"plaintext": "Proposition 2 established that a rise in D1 does not guarantee a rise in D3. The same non-conservation operates in reverse. D1 falls; D3 stays above threshold — for a while. This delay is density hysteresis."
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"plaintext": "The analogy to physical hysteresis is exact. A ferromagnet retains magnetization after the external field is removed. D3 persists as residual context-sharing after D1, the external input, has diminished."
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"plaintext": "Corollary 4.1 (Contracting Scene)"
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"plaintext": "The original essay defined four states: Death, False Growth, Comfortable Stagnation, Scene. Proposition 4 demands a fifth."
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"plaintext": "Contracting Scene — D1 is declining. D3 remains above threshold but is falling. The space is alive. On borrowed time."
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"plaintext": "When the hysteresis runs out, D3 crosses below threshold. A Contracting Scene is a transit state toward Death. Not irreversible: if D1 rises again, D3 decline can halt. But D3 does not recover on its own without renewed D1 input."
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"plaintext": "Corollary 4.2 (Performative Proof)"
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"plaintext": "A declaration that a space is dying sometimes generates massive cross-context engagement. Participants from unrelated contexts converge on a single topic and produce context-aware responses. This happens."
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"plaintext": "The phenomenon is observational evidence that D3 > threshold. The death declaration produces proof of life — a performative contradiction."
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"plaintext": "This does not refute the decline in D1. It confirms hysteresis. A Contracting Scene is exactly the state that generates performative contradictions: the numbers are falling, but the space still responds. That it still responds does not guarantee it will keep responding."
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"plaintext": "Open Question 2"
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"plaintext": "What determines the duration of hysteresis?"
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"plaintext": "Three candidates."
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"plaintext": "a. Peak D1. Higher peaks accumulate more context-sharing. More residual. Longer delay."
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"plaintext": "b. Duration at peak. A brief spike builds shallow context-sharing. A sustained high-density period builds deep context-sharing. Depth, not height, may govern persistence."
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"plaintext": "c. Internal structure of D3. Of the three components — identity, role, sustained anticipation — sustained anticipation depends on post flow and is the most fragile. Role awareness depends on recognition from others and is more durable. Identity is rooted in self-concept and is the most persistent — but when belonging to a space drops out of self-concept, collapse is irreversible."
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"plaintext": "Verification methods for these candidates remain undefined."
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"publishedAt": "2026-04-06T01:10:15+00:00",
"textContent": "The original essay (Three Densities) separated platform density into three layers and showed that conversion between them is non-conservative. The state classification there is static: it maps a platform at a single moment. This note introduces time.\nProposition 4 (Density Hysteresis)\nD3 responds to a decline in D1 with delay.\nWhen D1 is high, participants form context-sharing networks: mutual recognition, role awareness, shared reference points. These do not collapse the moment D1 drops. They are cumulative structures.\nProposition 2 established that a rise in D1 does not guarantee a rise in D3. The same non-conservation operates in reverse. D1 falls; D3 stays above threshold — for a while. This delay is density hysteresis.\nThe analogy to physical hysteresis is exact. A ferromagnet retains magnetization after the external field is removed. D3 persists as residual context-sharing after D1, the external input, has diminished.\nCorollary 4.1 (Contracting Scene)\nThe original essay defined four states: Death, False Growth, Comfortable Stagnation, Scene. Proposition 4 demands a fifth.\nContracting Scene — D1 is declining. D3 remains above threshold but is falling. The space is alive. On borrowed time.\nWhen the hysteresis runs out, D3 crosses below threshold. A Contracting Scene is a transit state toward Death. Not irreversible: if D1 rises again, D3 decline can halt. But D3 does not recover on its own without renewed D1 input.\nCorollary 4.2 (Performative Proof)\nA declaration that a space is dying sometimes generates massive cross-context engagement. Participants from unrelated contexts converge on a single topic and produce context-aware responses. This happens.\nThe phenomenon is observational evidence that D3 > threshold. The death declaration produces proof of life — a performative contradiction.\nThis does not refute the decline in D1. It confirms hysteresis. A Contracting Scene is exactly the state that generates performative contradictions: the numbers are falling, but the space still responds. That it still responds does not guarantee it will keep responding.\nOpen Question 2\nWhat determines the duration of hysteresis?\nThree candidates.\na. Peak D1. Higher peaks accumulate more context-sharing. More residual. Longer delay.\nb. Duration at peak. A brief spike builds shallow context-sharing. A sustained high-density period builds deep context-sharing. Depth, not height, may govern persistence.\nc. Internal structure of D3. Of the three components — identity, role, sustained anticipation — sustained anticipation depends on post flow and is the most fragile. Role awareness depends on recognition from others and is more durable. Identity is rooted in self-concept and is the most persistent — but when belonging to a space drops out of self-concept, collapse is irreversible.\nVerification methods for these candidates remain undefined."
}