Encyclopedia/All topics/Holography

Holography

Articles 61–120 of 224. Alphabetical by title.

• Holography Gibbs Casini Bound Gibbs Inequality

  The Gibbs inequality says the entropy of a distribution never exceeds its cross-entropy against any reference. Recognition Science's machine-checked library proves it for fini

• Holography Gibbs Casini Bound Gibbs Reference Pos

  A small theorem about a thermal reference state guarantees that every record in a finite ledger gets a positive probability, a necessary precondition for measuring information.

• Holography Gibbs Casini Bound Modular Hamiltonian Of Gibbs Reference

  A machine-checked theorem shows that when a reference state takes the Gibbs form, its modular Hamiltonian prices each record linearly by energy, a step toward a general entropy bou

• Holography Gibbs Casini Bound Relative Entropy Nonneg

  A single inequality, Gibbs's inequality, guarantees that a certain measure of disagreement between two probability distributions is never negative.

• Holography Gibbs Casini Bound Shannon Entropy Uniform Two

  A machine-checked proof that a two-outcome system with equal chances has exactly log 2 entropy, a small but necessary step in a larger physical bound.

• Holography Gibbs Uniqueness

  In statistical physics, the Gibbs state is the unique distribution that minimizes free energy at a fixed temperature; a machine-checked library now proves the same forcing result w

• Holography Gibbs Uniqueness Bekenstein Bound From Equilibrium

  A machine-checked proof shows that the exponential form of a thermal state, long assumed, is actually forced by a variational principle.

• Holography Gibbs Uniqueness Cross Entropy Gibbs State

  A machine-checked theorem shows that measuring the surprise of one probability distribution against another takes a specific, exact form when the second distribution is the Gibbs s

• Holography Gibbs Uniqueness Equilibrium Forces Gibbs Form

  Equilibrium, not assumption, is what gives a system its exponential probability law.

• Holography Gibbs Uniqueness Equilibrium Reference Nonvacuous

  A machine-checked theorem shows that the exponential Gibbs form is not assumed but forced by a free-energy minimization principle, and that the minimizer always exists.

• Holography Gibbs Uniqueness Gibbs Inequality Eq Iff

  In a finite system, the Gibbs inequality says entropy never exceeds cross-entropy; the new theorem tells exactly when the gap closes.

• Holography Gibbs Uniqueness Gibbs State Is Gibbs Reference

  The Gibbs state is the unique probability distribution that minimizes free energy, and its exponential form is a theorem, not an assumption.

• Holography Gibbs Uniqueness Partition Function Term Le One

  A small inequality about the partition function, the sum that defines statistical mechanics, turns out to be the hinge for a much larger uniqueness result.

• Holography Horizon Clock Rate

  Near a black hole's edge, a recognition clock advances at a fixed rate set by surface gravity, and a machine-checked library proves the rate law.

• Holography Horizon Clock Rate Clock Rate Bundle Silent On Period

  Near a black hole horizon, a clock's angle advances at a fixed rate; this theorem says that fact alone says nothing about when the clock completes a full turn.

• Holography Horizon Clock Rate Euclidean Angle Deriv Eq

  Near a black hole horizon, a recognition clock's angle advances at a fixed rate; the theorem proves the rate, not the full turn.

• Holography Horizon Clock Rate Euclidean Angle Rate

  A small theorem about a clock near a black hole horizon: the angle of its hands advances at a constant rate, and nothing more.

• Holography Horizon Clock Rate Legacy Horizon Rate Is Separate

  A machine-checked theorem in the Recognition Science library separates the abstract rate of a horizon clock from a specific normalization used in an older bridge, and proves the tw

• Holography Horizon Clock Rate Near Horizon Rindler Form

  Near a black hole's horizon, a recognition clock advances at a fixed rate; this declaration types exactly that rate and nothing more.

• Holography Horizon Clock Rate Period Is B2 Output Not B3 Input

  Near a black hole horizon, a clock's ticking rate is fixed by geometry, but the time for a full turn is a separate, derived fact.

• Holography Horizon Clock Rate Turn Ratio Unity At B2 Period

  A machine-checked theorem ties a horizon clock's full turn to a ratio of one, but only under a specific period it does not itself derive.

• Holography Horizon One Sided Cut

  A horizon hides its interior from view, and that one-sidedness forces the boundary to carry twice the information it would if the two sides could compare notes.

• Holography Horizon One Sided Cut Domino Face Capacity

  A single theorem in the framework's machine-checked library fixes the information capacity of a horizon pixel at 16 possible states, four bits, by counting how a one-sided cut

• Holography Horizon One Sided Cut Horizon Carries One Side Holds

  A machine-checked proof shows that a one-sided causal cut forces each side of a horizon to carry its own private copy of the shared edge record.

• Holography Horizon One Sided Cut Horizon One Sided Cut Cert

  A machine-checked theorem shows that when one side of a boundary cannot see the other, the shared edge records are counted twice, not once.

• Holography Horizon One Sided Cut Horizon Record Double Posts Seam

  A theorem about counting bits on a horizon shows why a shared edge gets recorded twice, once from each side, when one side of the cut is hidden.

• Holography Horizon One Sided Cut Kappa Per Pixel Is Four

  A machine-checked proof shows that when a horizon hides one side of a cut, each pixel on the boundary must carry four bits of information, not one.

• Holography Horizon One Sided Cut Marg A Image Univ

  A single global constraint on a divided system still lets each side read every possible local configuration, a fact that forces duplicated records at the boundary.

• Holography Horizon One Sided Cut Severed Edge Seam Is Two

  When a boundary is shared by two regions, each side must keep its own copy of the shared edge, and a machine-checked proof shows that doubles the count.

• Holography Keystone Factor Three

  A machine-checked argument that a black hole's entropy cannot be a count of its internal microstates, because that reading overshoots a fundamental bound by exactly three time

• Holography Keystone Factor Three Factor Three Is Ledger Forced

  A machine-checked proof shows a certain way of counting horizon states must assign exactly three times the entropy of another, and that this ratio is forced by the framework's

• Holography Keystone Factor Three Keystone Selects Record Reading

  A machine-checked theorem shows that if a black hole's entropy counts its record, the Bekenstein bound is met exactly, but if it counts microstates, the same bound is violated

• Holography Keystone Factor Three Microstate Chain Contradicts Bound

  A machine-checked argument shows that counting a black hole's entropy by its microstates violates a fundamental bound by exactly three times, unless a key physical premise is

• Holography Keystone Factor Three Microstate Reading Violates

  A machine-checked theorem shows that one common way to count black hole entropy would violate a fundamental bound by a factor of exactly three, but only if two unproved assumptions

• Holography Keystone Factor Three Record Chain Saturates Bound

  A machine-checked theorem shows one way of counting a black hole horizon's entropy hits the Bekenstein bound exactly, while a rival counting misses it by a fixed factor of thr

• Holography Keystone Factor Three Violation Is Scale Free

  A machine-checked theorem shows that if a certain entropy reading breaks a fundamental bound, it breaks it by exactly the same factor at every horizon size.

• Holography Keystone Factor Three Violation Survives Unit Conversion

  A machine-checked theorem shows that a specific violation of a fundamental entropy bound cannot be argued away by switching from bits to nats.

• Holography Kmsdetailed Balance Bekenstein Bound From Kms

  A theorem in the framework's machine-checked library derives the Bekenstein bound from three plain dynamical assumptions, not from an assumed equilibrium state.

• Holography Landauer Bridge Walls

  A machine-checked ledger shows exactly where the physics of heat and the physics of information remain unconnected.

• Holography Landauer Bridge Walls Clausius Step Heat Is One Channel Posting

  The declaration pins down what counts as a heat step in the framework's ledger, and it carefully does not claim to have measured any heat.

• Holography Landauer Bridge Walls Landauer Bridge Wall Cert

  A machine-checked certificate that marks exactly where the Landauer principle is proven and where it remains a hypothesis.

• Holography Landauer Bridge Walls Logical Erasure Posts Debit Iff

  A theorem in the Recognition Science library pins down what it means for a computation to erase a bit: it is a bookkeeping statement, not a physical reset.

• Holography Landauer Bridge Walls One Bit Erasure Fails On Idle

  A machine-checked proof shows that claiming a one-bit logical erasure on a path that does nothing is false, a small but sharp test of what counts as erasure.

• Holography Landauer Bridge Walls Posting Step Target Posts Nonzero

  A single vertex flip in a discrete cell grid is enough to show that a zero heat carrier cannot account for the framework's posted records.

• Holography Landauer Bridge Walls Tautological Heat Is Posted Record Flux

  A machine-checked theorem shows that defining heat as posted record flux satisfies the framework's heat premise, but only by definition, not by physical measurement.

• Holography Landauer Bridge Walls Zero Bits Erasure On Idle

  A machine-checked theorem confirms that a system that does nothing erases zero bits, and that claiming otherwise is false.

• Holography Landauer Calorimeter Descent

  A machine-checked proof that a cell's posted heat is exactly the sum of its six face-channel heats, and that no smaller set of channels can serve.

• Holography Landauer Calorimeter Descent Face Record Eq Face Bits

  A machine-checked theorem shows that the six faces of a cell in Recognition Science are exactly the six binary readings of its corners, and nothing more.

• Holography Landauer Calorimeter Descent Five Channel Sum Ne Step Heat Cell

  A machine-checked proof shows that omitting one face from a six-sided heat count breaks the ledger, and that the omission is not a mere rounding error.

• Holography Landauer Calorimeter Descent Heat Carrier Unique

  In the Recognition Science framework, a machine-checked theorem proves that only one way exists to assign heat to a step in a cellular ledger, and it does not claim to build a phys

• Holography Landauer Calorimeter Descent Landauer Calorimeter Descent Cert

  A machine-checked proof that heat flow through a cube's six faces exactly matches the posted ledger entry, while honestly recording that this is not an independent measurement

• Holography Landauer Calorimeter Descent Six Channel Heat Eq Scaled Step Heat Cel

  A machine-checked proof shows that a cell's posted heat is exactly the sum of its six face-channel heats, and that this identity is a theorem, not a definition.

• Holography Landauer Calorimeter Descent Six Channel Heat Is Posted Record Flux

  A formal proof shows that heat, defined as the sum of six face-channel contributions, is exactly the posted record flux of a cell, with a strict limit on what that identity means.

• Holography Landauer Calorimeter Descent Step Heat Cell Eq Sum Face Channels

  A machine-checked proof shows that the heat of a cell is exactly the sum of its six faces, but it is a bookkeeping identity, not a new law of physics.

• Holography Landauer Calorimeter Forcing

  A machine-checked library shows that a proposed rule for counting heat in a discrete ledger cannot be forced into existence, naming the missing piece as an open target.

• Holography Landauer Calorimeter Forcing Double Posted Heat Face Additive

  A machine-checked proof shows a doubled heat value passes weak axioms but fails as a real calorimeter, marking an open gap.

• Holography Landauer Calorimeter Forcing Double Posted Heat Ne Unit Tautological

  A machine-checked proof shows why a seemingly natural way to define heat in a discrete ledger fails, and names the missing ingredient.

• Holography Landauer Calorimeter Forcing Logical Protocol Refuses Idle One Bit

  A machine-checked proof shows a protocol that erases nothing cannot claim to have erased one bit, while carefully leaving the harder physics open.

• Holography Landauer Calorimeter Forcing Missing Independent Cell Calorimeter Wal

  A machine-checked proof that a proposed physical law cannot be derived from its own definitions, and that a specific gap remains open.

• Holography Landauer Calorimeter Forcing Smuggling Package Eq Tautological

  A machine-checked proof shows that a natural way to define heat in a cellular ledger secretly assumes the answer it claims to derive.