RedTail experiments with entropy qubits radiation and reflection

Research record, 5 October 2026. The user requested a return to RedTail-X and trials involving event-horizon entropy, qubits, Hawking radiation, and the Refracting Light proposal. This experiment constructs explicit toy adaptations of those ideas and compares their 64-bit outputs. The revised integer Refracting Light performed substantially better in these limited statistical checks. No candidate has established cryptographic security or physical black-hole decoding.

Relationship to the existing RedTail formula

The input stage reuses clamp_trials.encode, the existing Python reproduction of the project’s variable-tail layout and custom parity rows. For message length t, the shard size is ceil(t/4). Four systematic data shards and two GF(256) parity shards are emitted. The parity rows are [1,1,1,1] and [1,2,3,4], using the field polynomial 0x11d. These match the custom arithmetic inspected in DarkRock/src/polynomial_code.rs; this is not an assertion that every RS library uses that matrix.

The experimental record is the original length as eight big-endian bytes followed by all six shards in order. It retains the input and length. Every two-byte input in the exhaustive census was recovered from this record exactly. Original project sources were read, not modified.

The production clamp in DarkRock/src/representation.rs guards log2(p) in an entropy estimate. It is not an RS field boundary or an event horizon. It remains unchanged. A separate reflecting boundary implements the requested Refracting Light trial. No ABS mapping of message digits was introduced.

All candidates produce 64 bits. No cryptographic hash is hidden inside a candidate. SHA-256 truncated to its first eight bytes is used only as a separately labelled comparator, applied to the same record.

Physical equations and our adaptations

For a Schwarzschild black hole, the horizon area and entropy obey A = 16piG^2M^2/c^4 and S_BH = k_Bc^3A/(4Ghbar). Thus entropy scales as M squared. Hawking temperature is T_H = hbarc^3/(8piGMk_B), inversely proportional to M. These are equilibrium formulas, not cryptographic constructions. Wald, The Thermodynamics of Black Holes and Hawking, Particle creation by black holes.

The choices below are new experimental mappings, not formulas proposed by those authors. Let Q = 2^64−1 and let x be the record’s polynomial accumulator. The chosen mass ratio is m = M/M0 = 1+x/Q, in [1,2]. No astronomical mass is assigned to message bytes.

Variant	Exact experimental rule
Polynomial control	Start x=0; for each record byte b, x=(257*x+b+1) modulo 2^64.
Area entropy	floor[x*(2Q+x)/(3Q)]. This is Q times the normalized area ratio (m^2−1)/3. Uses exact integer arithmetic.
Hawking temperature	floor[Q^2/(Q+x)], representing Q/m. Uses exact integer arithmetic.
Hawking occupation	floor[Q/(exp(m)−1)], a chosen ideal bosonic mode with greybody factor one and hbaromega/(k_BT0)=1. Uses floating point.
Qubit probabilities	A two-qubit pure-state circuit consumes the entire record; its four output probabilities are each quantized to 16 bits and concatenated.
Refracting Light variants	A reflecting integer interval, velocity update, and escape feedback consume the whole record. Definitions below.
Combined variants	Feed the original record followed by eight bytes each of area, temperature, occupation, and qubit outputs into a Refracting Light variant.

The Hawking occupation experiment uses one idealized mode, not a complete emission spectrum, an evaporation simulation, or a neutrino scattering calculation. The combined construction includes all the original record, so it does not rely on those scalar summaries retaining the message.

Qubit definition

Initialize |00>. For byte b at zero-based position i, apply RY(theta) on qubit 0, RZ(phi) on qubit 1, then CNOT(0,1). Define theta = 2pi(b+1)/257 and phi = 2pi(((i+1)(b+1)) mod 263)/263. Output p_j = real(amplitude_j)^2 + imag(amplitude_j)^2, normalized for floating-point drift, followed by q_j=floor(65535p_j).

This uses a classical simulation of quantum-state evolution and Born probabilities. It does not use a quantum processor or sample physical measurements. The probability rule follows the standard statevector formalism; this particular gate sequence is our design. IBM Quantum learning material.

For the Hello World input, two independent measurements of this circuit would agree with probability approximately 79.37%, calculated as sum(p_j^2). That is a repeatability diagnostic for sampled outcomes, not for the deterministic probability-vector calculation. A single shot returns a two-bit outcome, not a 64-bit digest. Floating-point versions are reproducible in the tested environment but lack a cross-platform consensus specification.

Refracting Light definition and targeted revision

This is a proposed integer reflection model. It is not a model of a white hole or a demonstrated physical escape mechanism. Let L=2^32−1. For signed integer z, obtain q,r=divmod(z,L), then:

y = r          if q is even
y = L − r      if q is odd

Here y is the rebound position and q records which interval z occupied, including negative intervals. The exact inverse is z=qL+y for even q, or z=qL+(L−y) for odd q. We tested the inverse for 20,001 signed integers.

The digest recurrence starts at position x=0 and velocity v=1. For each byte b at position i:

z = 257*x + 17*v + (b+1)*(i+1)
x, q = fold(z)
v = (65537*v + q + b + i + 1) modulo 2^32
x = x XOR ROTL32(v, (i modulo 31)+1)

Return x concatenated with v. The drop-escape control replaces q with zero in the velocity update. The original feedback version includes q. It does not retain a lossless history of all q values: a final 64-bit state still compresses arbitrary messages.

The first run exposed weak low bits. Since 65537 is 1 modulo 65536, the low 16 velocity bits mainly accumulated sums. A targeted revision inserts this line immediately before the final position XOR:

v = ROTL32(v, 13) XOR x

This revised rule is labelled rotated feedback. The constants and rotation are experimental design choices. The same fixed test sets were rerun to check the identified weakness; these are not held-out validation results.

Test design

• Exhaustively enumerate all 65,536 two-byte messages; count collisions in the full 64-bit output and separately in its low 16 bits.

• Flip each of 128 bits in 32 seeded, 16-byte messages: 4,096 comparisons per variant. Measure total bit changes and each output bit’s change rate.

• Enumerate 65,536 nonce values appended as eight big-endian bytes to Hello World. Test 8, 10, and 12 leading-zero-bit targets.

• Check complete-record restoration, signed reflection inverses, same-environment repeatability, and the previously known parity-only collision.

All input choices are reproducible; the perturbation seed is 20261005. Scalar functions, qubit gates, and rebound recurrences are stateless between messages. There is no secret key or fresh salt. Tests do not assess key security or decryption.

Measured results

No full 64-bit collisions occurred in the two-byte census for any variant, including the weak polynomial control. With only 65,536 inputs, a uniform 64-bit function would have about 1.16e−10 expected colliding pairs. The absence of such collisions provides little security evidence. A uniform low-16-bit projection instead has 32,767.5 expected colliding pairs at this census size.

Variant	Mean changed bits of 64	Low 16-bit colliding pairs	Target hits for 8 / 10 / 12 zero bits
Polynomial control	27.771	23,509	251 / 61 / 15
Area entropy	31.995	32,935	381 / 88 / 24
Hawking temperature	31.559	32,409	0 / 0 / 0
Hawking occupation	27.025	16,768,112	0 / 0 / 0
Qubit probabilities	29.853	75,278	1,680 / 509 / 141
Refracting Light dropping escape	22.007	4,540,866	263 / 65 / 19
Refracting Light with escape feedback	28.512	2,883,299	267 / 69 / 14
Combined original	30.415	1,022,924	246 / 62 / 10
Refracting Light with rotated feedback	32.123	33,004	257 / 54 / 13
Combined with rotated feedback	31.937	32,840	284 / 81 / 17
SHA-256 truncated reference	31.979	33,046	208 / 60 / 20
Uniform expectation	32	32,767.5	256 / 64 / 16

Target counts are one finite nonce sweep, not proof of uniformity, independent trials, or expected mining cost. In particular the SHA reference’s 208 hits are not a weaker security result than a candidate’s count closer to 256. A public target can be attached to any output; its existence does not establish a hard search problem.

The revised Refracting Light had per-output-bit flip rates from 48.34% to 53.17%; the revised combination ranged from 48.54% to 51.59%. No output bit remained unchanged throughout their perturbation tests. The original combined version had one such bit, the original feedback Refracting Light two, and the drop-escape version three. These are observed sample properties, not mathematical invariants for every input.

What the failures reveal

Entropy alone is not a hardness mechanism. The area mapping achieved almost 32 changed bits on average but biased the leading-zero target. Its underlying function is monotone and can be inverted or searched by elementary arithmetic. Quantization already merges scalar x=0 and x=1. Those scalar-stage collisions are not claims of discovered complete-message collisions.

Temperature and occupation are range constrained. Our normalized temperature digest occupies roughly the upper half of the unsigned range, and occupation stays above about 15.65% of it. Neither can reach an eight-leading-zero-bit target in this specification. Changing the output scaling changes this result, so this is a failure of these concrete mappings, not a universal impossibility claim about radiation-inspired constructions. Floating-point occupation also leaves at least nine low bits zero at these magnitudes.

A probability vector is a lossy summary. The four quantized qubit probabilities must nearly sum to 65535. With exact probabilities their integer sum lies in 65532–65535, constraining the nominal 64-bit word to at most about 2^47.4 possibilities. The two-qubit state evolution is also efficiently simulated classically. There is no quantum hardness result here.

Reflection alone merges trajectories. For L=31, z=5 and z=57 both return y=5, but their escape indices are 0 and 1. Across −1000 through 1000, saturation and reflection alone each produced 32 distinct positions. The pair (position, escape index) retained all 2,001 inputs. The new feedback digest uses this escape information internally; it does not turn the fixed-length digest into a reversible representation of arbitrary messages.

The revised feedback repairs the observed low-bit weakness. It brings these statistical measurements close to the reference. This only supports further investigation: no collision attack, preimage attack, differential analysis, cycle analysis, or quantum attack bound has established security. The combined model also inherits floating-point reproducibility problems from its qubit and occupation components.

Assessment

The integer Refracting Light with rotated escape feedback is the clearest next research subject: it is fully specified with integer arithmetic, preserves the proposed rebound/escape behavior, and passes these limited distribution checks. The combined variant did not demonstrate a security advantage over it. Full 256-bit design and cryptanalysis would be separate work; a nominal 64-bit hash cannot provide SHA-256’s generic collision strength.

These trials support neither a physical white-hole Refracting Light nor a SHA-256 replacement. They do establish a concrete, reproducible difference between dropping boundary-crossing information, feeding it back weakly, and mixing that feedback through the state.

Artifacts

• redtail_physics_trials.py: complete formulas and executable experiment. Uses the Python standard library and the existing clamp_trials.py.

• redtail-physics-results.json: full precision measurements, target hits and first accepted nonces, probability diagnostics, and example digests.

• Run python3 redtail_physics_trials.py from this directory to reproduce the experiment.

The experimental record and digest formats are defined by the code. They are exploratory formats, not a published network protocol.