pith. machine review for the scientific record. sign in

arxiv: 2605.02792 · v2 · submitted 2026-05-04 · ✦ hep-th · gr-qc· quant-ph

Recognition: 2 theorem links

· Lean Theorem

Albertian Channel Memory in Black-Hole Evaporation

Rafael B. Frigori
Authors on Pith no claims yet

Pith reviewed 2026-05-13 01:59 UTC · model grok-4.3

classification ✦ hep-th gr-qcquant-ph
keywords black hole evaporationAMPS paradoxAlbert algebraVolterra memory lawoctonionic supergravityPage curvePeirce decompositionHawking radiation
0
0 comments X

The pith

Black hole evaporation produces ordinary radiation with exceptional memory imprinted by the horizon algebra rather than restoring AMPS tensor factorization.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper establishes that modeling the black hole horizon with the Albert algebra from a retained sector of octonionic magical supergravity allows a Peirce decomposition of the data into hidden, relay, and exterior parts. Eliminating the relay sector yields a source-fixed Volterra memory law along the evaporation trajectory. This law imprints the radiation as a two-time coherence in helicity observables while preserving ordinary emitted readout. A sympathetic reader would care because the construction keeps standard quantum mechanics on associative blocks and reconstructs the Page curve envelope from Euclidean endpoint actions without invoking non-local tensor factorization.

Core claim

By taking the retained attractor sector whose horizon symbols form the Albert algebra J3(O), states become positive normalized functionals, events become Jordan idempotents, and reversible motions become algebra automorphisms. Peirce theory then splits the horizon data, and removal of the interface relay produces a source-fixed Volterra memory law on the neutral-source fixed-charge Reissner-Nordstrom trajectory. In real time the leading occupation follows the evaporation clock while retained memory appears as spectral-overlap two-time coherence of windowed helicity observables; in Euclidean time the kernel admits Tsallis/Lomax and shifted-Levy branches whose lower envelope reconstructs the 0

What carries the argument

The Albert algebra J3(O) realized by horizon symbols in the retained attractor sector, which supplies the Peirce decomposition that isolates the hidden complement, interface relay, and exterior detector and thereby induces the source-fixed Volterra memory law.

If this is right

  • The leading one-time occupation of the emitted radiation follows the sourced evaporation clock in real time.
  • Retained memory appears as a spectral-overlap connected two-time coherence of windowed helicity and Stokes observables.
  • In Euclidean time the Peirce-Volterra kernel exhibits a regular-opening Tsallis/Lomax onset and a near-extremal shifted-Levy residence branch.
  • The lower admissible envelope of the endpoint actions reconstructs the Page-curve envelope.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Similar non-associative algebraic structures could be explored in other gravitational models to embed memory directly in radiation channels.
  • Two-time correlation measurements in Hawking spectra at future detectors could serve as a concrete test of the predicted coherence imprint.
  • The construction suggests that exceptional Jordan algebras may provide a systematic way to retain information in evaporating systems while keeping local readout ordinary.

Load-bearing premise

The retained attractor sector of octonionic magical supergravity has horizon symbols that form the Albert algebra J3(O), allowing Peirce theory to split the data and induce a source-fixed Volterra memory law.

What would settle it

Observation of a two-time coherence function in the helicity or Stokes parameters of the emitted radiation whose spectral overlap matches the Volterra kernel but deviates from pure thermal Hawking statistics at the predicted time scales.

Figures

Figures reproduced from arXiv: 2605.02792 by Rafael B. Frigori.

Figure 1
Figure 1. Figure 1: FIG. 1. Schematic summary of the channel-memory archi view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Neutral-source fixed-charge Reissner–Nordström view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Reduced-channel entropy and dephased qubit surro view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Reduced-channel entropy and dephased qubit surro [PITH_FULL_IMAGE:figures/full_fig_p012_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Channel relay scales and reduced-state transport view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Fixed-support photonic two-time forecast on the sourced RN clock. Left: the spectral overlap view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Source-fixed branch-envelope reconstruction from view at source ↗
read the original abstract

The AMPS paradox assumes a globally associative tensor-product stage for the early radiation, the exterior Hawking mode, and the interior partner. We study a retained attractor sector of octonionic magical supergravity whose horizon symbols form the Albert algebra J3(O). This induces an Albertian algebraic-quantum description: states are positive normalized functionals, events are Jordan idempotents, reversible motions are algebra automorphisms, and ordinary quantum mechanics is recovered on associative readout blocks. Peirce theory then splits the horizon data into a hidden exceptional complement, an interface relay, and a two-helicity exterior detector. Eliminating the relay gives a source-fixed Volterra memory law on a neutral-source fixed-charge Reissner--Nordstrom evaporation trajectory. In real time, the leading one-time occupation follows the sourced evaporation clock, while the retained-memory imprint appears as a spectral-overlap connected two-time coherence of windowed helicity/Stokes observables in the emitted history. In Euclidean time, the Peirce--Volterra kernel becomes a transfer kernel with two branchwise superstatistical limits: a regular-opening Tsallis/Lomax onset and a near-extremal shifted-Levy residence branch. The lower admissible envelope of the endpoint actions then reconstructs the Page-curve envelope. The result is an ordinary emitted readout with exceptional memory, not a restored AMPS tensor factorization.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 0 minor

Summary. The paper claims that in a retained attractor sector of octonionic magical supergravity, horizon symbols form the Albert algebra J3(O), inducing an algebraic-quantum description with states as positive functionals, events as idempotents, and motions as automorphisms. Peirce decomposition splits horizon data into hidden exceptional complement, interface relay, and two-helicity exterior detector; eliminating the relay produces a source-fixed Volterra memory law on the RN evaporation trajectory. This yields one-time occupation following the sourced clock and two-time helicity/Stokes coherence in the emitted history. In Euclidean time the kernel has Tsallis/Lomax and shifted-Levy branches, with the lower envelope of endpoint actions reconstructing the Page curve. The result is framed as ordinary emitted readout with exceptional memory, not restored AMPS factorization.

Significance. If the algebraic-to-physical mapping were rigorously derived, the work would supply a non-associative Jordan-algebraic mechanism for memory effects in evaporation that recovers ordinary QM on associative blocks and produces a Page-curve envelope from endpoint actions. It offers a concrete alternative to tensor-factorization resolutions and introduces potentially falsifiable signatures in windowed helicity observables. These strengths are currently offset by the absence of explicit derivations, leaving the significance conditional on verification that the Volterra kernel emerges from the J3(O) structure constants rather than being imposed.

major comments (3)
  1. [Abstract] Abstract: the assertion that 'Peirce theory then splits the horizon data... Eliminating the relay gives a source-fixed Volterra memory law' is presented without any displayed equation, multiplication table, or structure-constant calculation showing how the non-associative product in J3(O) fixes the kernel coefficients on the neutral-source RN trajectory.
  2. [Abstract] Abstract: the reconstruction 'the lower admissible envelope of the endpoint actions then reconstructs the Page-curve envelope' is load-bearing for the central claim yet appears to follow by construction once the retained attractor sector and Volterra kernel are chosen; no independent check or falsifiable prediction is supplied to separate this from parameter tuning.
  3. [Abstract] Abstract: the weakest assumption—that 'horizon symbols form the Albert algebra J3(O) in the retained attractor sector'—is stated axiomatically with no derivation linking the octonionic magical supergravity attractor to the Jordan algebra projectors or to the Stokes observables; without this step the subsequent Peirce–Volterra induction cannot be verified.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the thorough review and insightful comments on our manuscript. We address each of the major comments in detail below and outline the revisions we plan to implement to strengthen the clarity and rigor of the presentation.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the assertion that 'Peirce theory then splits the horizon data... Eliminating the relay gives a source-fixed Volterra memory law' is presented without any displayed equation, multiplication table, or structure-constant calculation showing how the non-associative product in J3(O) fixes the kernel coefficients on the neutral-source RN trajectory.

    Authors: We thank the referee for pointing this out. The abstract is necessarily concise and omits the explicit calculations. In the full manuscript, the Peirce decomposition is applied to the Albert algebra J3(O) using its standard multiplication table and structure constants (detailed in Section 2), which determine the coefficients of the Volterra integral kernel on the fixed-charge RN evaporation trajectory. The non-associative product induces the memory term through the off-diagonal Peirce components after eliminating the relay sector. We will revise the abstract to include a parenthetical reference to the relevant structure constants and equation numbers from the main text. revision: yes

  2. Referee: [Abstract] Abstract: the reconstruction 'the lower admissible envelope of the endpoint actions then reconstructs the Page-curve envelope' is load-bearing for the central claim yet appears to follow by construction once the retained attractor sector and Volterra kernel are chosen; no independent check or falsifiable prediction is supplied to separate this from parameter tuning.

    Authors: The envelope reconstruction is derived from the specific form of the Euclidean transfer kernel, whose branches are fixed by the Tsallis/Lomax and shifted-Levy limits of the superstatistical Volterra kernel on the RN trajectory. It is not a free parameter but emerges from the endpoint actions in the retained sector. To address the concern, we will include in the revised manuscript an explicit comparison plot of the reconstructed envelope against the standard Page curve for a range of black hole parameters, along with a discussion of how the two-time helicity coherence provides a falsifiable signature distinguishable from standard models. revision: yes

  3. Referee: [Abstract] Abstract: the weakest assumption—that 'horizon symbols form the Albert algebra J3(O) in the retained attractor sector'—is stated axiomatically with no derivation linking the octonionic magical supergravity attractor to the Jordan algebra projectors or to the Stokes observables; without this step the subsequent Peirce–Volterra induction cannot be verified.

    Authors: The identification of the horizon symbols with J3(O) follows from the Jordan algebraic formulation of the scalar sector in octonionic magical supergravity, where the attractor mechanism selects a sector whose charge vectors correspond to the idempotents of the Albert algebra. The link to Stokes observables arises because the two-helicity exterior detector corresponds to the Peirce subspace associated with the off-diagonal elements. We agree that this foundational step requires more explicit exposition. In the revision, we will add a dedicated subsection in the introduction deriving the correspondence between the supergravity attractor equations, the Jordan projectors, and the Stokes parameters. revision: yes

Circularity Check

1 steps flagged

Peirce split of J3(O) and relay elimination define Volterra kernel to reconstruct Page curve by construction

specific steps
  1. self definitional [Abstract]
    "Peirce theory then splits the horizon data into a hidden exceptional complement, an interface relay, and a two-helicity exterior detector. Eliminating the relay gives a source-fixed Volterra memory law on a neutral-source fixed-charge Reissner--Nordstrom evaporation trajectory. ... The lower admissible envelope of the endpoint actions then reconstructs the Page-curve envelope."

    The Peirce split into complement/relay/detector is introduced on J3(O), and 'eliminating the relay' is stated to produce the Volterra law; the endpoint actions are then defined such that their lower envelope matches the known Page curve. The memory law and its observable effect are therefore constructed to deliver the target reconstruction rather than derived from independent algebraic or geometric inputs.

full rationale

The central derivation asserts that the Albert algebra J3(O) on the retained attractor sector, via Peirce decomposition, directly yields a source-fixed Volterra memory law whose endpoint actions reconstruct the Page curve. This reduces the claimed physical memory effect to a quantity fixed by the choice of algebraic sector, split, and elimination rule rather than an independent derivation from structure constants or geometry. The abstract presents the induction as immediate ('Eliminating the relay gives...') and the reconstruction as following ('then reconstructs'), satisfying the self-definitional pattern with no external benchmark or explicit mapping shown.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 2 invented entities

The central claim rests on the assumption that the horizon carries an Albert algebra structure and on several new concepts introduced to produce the memory law; these are not derived from prior literature but postulated for this application.

free parameters (1)
  • window parameters for helicity/Stokes observables
    Control the two-time coherence in the emitted history and are not fixed by the algebra.
axioms (2)
  • ad hoc to paper Horizon symbols form the Albert algebra J3(O) in the retained attractor sector
    Invoked at the outset to induce the algebraic-quantum description.
  • domain assumption States are positive normalized functionals, events are Jordan idempotents, motions are automorphisms
    Defines the algebraic-quantum framework used throughout.
invented entities (2)
  • Albertian channel memory no independent evidence
    purpose: Provides retained memory imprint in the radiation
    New concept introduced to replace AMPS tensor factorization.
  • hidden exceptional complement and interface relay no independent evidence
    purpose: Peirce split of horizon data
    Postulated components whose elimination yields the Volterra law.

pith-pipeline@v0.9.0 · 5536 in / 1687 out tokens · 47813 ms · 2026-05-13T01:59:43.657179+00:00 · methodology

Review history (2 revisions) →

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

102 extracted references · 102 canonical work pages

  1. [1]

    S. W. Hawking, Communications in Mathematical Physics43, 199 (1975)

    work page 1975

  2. [2]

    D. N. Page, Physical Review Letters71, 3743 (1993)

    work page 1993

  3. [3]

    Almheiri, D

    A. Almheiri, D. Marolf, J. Polchinski, and J. Sully, JHEP 2013(2), 062

    work page 2013

  4. [4]

    Harlow, Reviews of Modern Physics88, 015002 (2016)

    D. Harlow, Reviews of Modern Physics88, 015002 (2016)

    work page 2016

  5. [5]

    Almheiri, T

    A. Almheiri, T. Hartman, J. Maldacena, E. Shaghoulian, and A. Tajdini, JHEP2020(05), 013, arXiv:1911.12333 [hep-th]

    work page arXiv 1911

  6. [6]

    Almheiri, T

    A. Almheiri, T. Hartman, J. Maldacena, E. Shaghoulian, and A. Tajdini, Reviews of Modern Physics93, 035002 (2021)

    work page 2021

  7. [7]

    Penington, JHEP2020(9), 002

    G. Penington, JHEP2020(9), 002

    work page

  8. [8]

    Local subsystems in gauge theory and gravity

    W. Donnelly and L. Freidel, JHEP2016(09), 102, arXiv:1601.04744 [hep-th]

    work page Pith review arXiv

  9. [9]

    Donnelly and S

    W. Donnelly and S. B. Giddings, Phys. Rev. D96, 086013 (2017), arXiv:1706.03104 [hep-th]

    work page arXiv 2017

  10. [10]

    Lessons from the information paradox,

    S. Raju, Phys. Rept.943, 1 (2022), arXiv:2012.05770 [hep-th]

    work page arXiv 2022

  11. [11]

    Jordan, J

    P. Jordan, J. von Neumann, and E. P. Wigner, Annals of Mathematics35, 29 (1934)

    work page 1934

  12. [12]

    A. A. Albert, Annals of Mathematics35, 65 (1934)

    work page 1934

  13. [13]

    McCrimmon,A Taste of Jordan Algebras(Springer, New York, 2004)

    K. McCrimmon,A Taste of Jordan Algebras(Springer, New York, 2004)

    work page 2004

  14. [14]

    I. E. Segal, Annals of Mathematics Second Series,48, 930 (1947)

    work page 1947

  15. [15]

    R.HaagandD.Kastler,JournalofMathematicalPhysics 5, 848 (1964)

    work page 1964

  16. [16]

    Haag,Local Quantum Physics: Fields, Particles, Al- gebras(Springer, Berlin, 1992)

    R. Haag,Local Quantum Physics: Fields, Particles, Al- gebras(Springer, Berlin, 1992)

    work page 1992

  17. [17]

    Günaydin, C

    M. Günaydin, C. Piron, and H. Ruegg, Communications in Mathematical Physics61, 69 (1978)

    work page 1978

  18. [18]

    Barnum and A

    H. Barnum and A. Wilce, Found. Phys.44, 192 (2014)

    work page 2014

  19. [19]

    Niestegge, Found

    G. Niestegge, Found. Phys.45, 525 (2015), arXiv:1402.0158 [math-ph]

    work page arXiv 2015

  20. [20]

    Günaydin, G

    M. Günaydin, G. Sierra, and P. K. Townsend, Physics Letters B133, 72 (1983)

    work page 1983

  21. [21]

    Günaydin, G

    M. Günaydin, G. Sierra, and P. K. Townsend, Nuclear Physics B242, 244 (1984)

    work page 1984

  22. [22]

    Ferrara and M

    S. Ferrara and M. Günaydin, Nuclear Physics B759, 1 (2006)

    work page 2006

  23. [23]

    Bianchi and S

    M. Bianchi and S. Ferrara, JHEP2008(2), 054

    work page

  24. [24]

    M. K. Parikh and F. Wilczek, Physical Review Letters 85, 5042 (2000), arXiv:hep-th/9907001 [hep-th]

    work page arXiv 2000

  25. [25]

    Gripenberg, S.-O

    G. Gripenberg, S.-O. Londen, and O. Staffans,Volterra Integral and Functional Equations(Cambridge Univer- sity Press, Cambridge, 1990)

    work page 1990

  26. [26]

    Papadodimas and S

    K. Papadodimas and S. Raju, J. High Energy Phys.2013 (10), 212, arXiv:1211.6767 [hep-th]

    work page arXiv 2013

  27. [27]

    Papadodimas and S

    K. Papadodimas and S. Raju, Phys. Rev. D93, 084049 (2016), arXiv:1503.08825 [hep-th]

    work page arXiv 2016

  28. [28]

    Harlow, J

    D. Harlow, J. High Energy Phys.2014(11), 055, arXiv:1405.1995 [hep-th]

    work page arXiv 2014

  29. [29]

    Witten,Gravity and the crossed product,JHEP10(2022) 008 [2112.12828]

    E. Witten, J. High Energy Phys.2022(10), 008, arXiv:2112.12828 [hep-th]

    work page arXiv 2022

  30. [30]

    Jensen, J

    K. Jensen, J. Sorce, and A. J. Speranza, J. High Energy Phys.2023(12), 020, arXiv:2306.01837 [hep-th]

    work page arXiv 2023

  31. [31]

    Faulkner and A.J

    T. Faulkner and A. J. Speranza, J. High Energy Phys. 2024(11), 099, arXiv:2405.00847 [hep-th]

    work page arXiv 2024

  32. [32]

    S.D.Mathur,ClassicalandQuantumGravity26,224001 (2009), arXiv:0909.1038 [hep-th]

    work page arXiv 2009

  33. [33]

    Anastopoulos and N

    C. Anastopoulos and N. Savvidou, Classical and Quan- tum Gravity37, 025015 (2020), arXiv:1909.00438 [gr-qc]

    work page arXiv 2020

  34. [34]

    S. B. Giddings, Physical Review D88, 064023 (2013), arXiv:1211.7070 [hep-th]

    work page arXiv 2013

  35. [35]

    S. W. Hawking, M. J. Perry, and A. Strominger, Physi- cal Review Letters116, 231301 (2016), arXiv:1601.00921 [hep-th]

    work page Pith review arXiv 2016

  36. [36]

    R. W. Lindquist, R. A. Schwartz, and C. W. Misner, Phys. Rev.137, B1364 (1965)

    work page 1965

  37. [37]

    W. B. Bonnor and P. C. Vaidya, Gen. Relativ. Gravit.1, 127 (1970)

    work page 1970

  38. [38]

    D. N. Page, Physical Review D13, 198 (1976)

    work page 1976

  39. [39]

    D. N. Page, Physical Review D14, 3260 (1976)

    work page 1976

  40. [40]

    W. A. Hiscock and L. D. Weems, Physical Review D41, 1142 (1990)

    work page 1990

  41. [41]

    Moncrief, Phys

    V. Moncrief, Phys. Rev. D10, 1057 (1974)

    work page 1974

  42. [42]

    Moncrief, Phys

    V. Moncrief, Phys. Rev. D12, 1526 (1975)

    work page 1975

  43. [43]

    F. J. Zerilli, Phys. Rev. D9, 860 (1974)

    work page 1974

  44. [44]

    Chandrasekhar,The Mathematical Theory of Black Holes(Oxford University Press, Oxford, 1983)

    S. Chandrasekhar,The Mathematical Theory of Black Holes(Oxford University Press, Oxford, 1983)

    work page 1983

  45. [45]

    Hod, Phys

    S. Hod, Phys. Rev. D93, 104027 (2016)

    work page 2016

  46. [46]

    Ngampitipan and P

    T. Ngampitipan and P. Boonserm, J. Phys.: Conf. Ser. 435, 012027 (2013)

    work page 2013

  47. [47]

    Beck and E

    C. Beck and E. G. D. Cohen, Physica A: Statistical Me- chanics and its Applications322, 267 (2003)

    work page 2003

  48. [48]

    Beck, Continuum Mechanics and Thermodynamics 16, 293 (2004)

    C. Beck, Continuum Mechanics and Thermodynamics 16, 293 (2004)

    work page 2004

  49. [49]

    Bernstein, Acta Mathematica52, 1 (1929)

    S. Bernstein, Acta Mathematica52, 1 (1929)

    work page 1929

  50. [50]

    D. V. Widder,The Laplace Transform(Princeton Uni- versity Press, Princeton, 1941)

    work page 1941

  51. [51]

    Beck, Contemporary Physics50, 495 (2009)

    C. Beck, Contemporary Physics50, 495 (2009)

    work page 2009

  52. [52]

    Tsallis, Journal of Statistical Physics52, 479 (1988)

    C. Tsallis, Journal of Statistical Physics52, 479 (1988)

    work page 1988

  53. [53]

    Tsallis,Introduction to Nonextensive Statistical Me- chanics: Approaching a Complex World(Springer, New York, 2009)

    C. Tsallis,Introduction to Nonextensive Statistical Me- chanics: Approaching a Complex World(Springer, New York, 2009)

    work page 2009

  54. [54]

    R. B. Frigori, Computer Physics Communications185, 2232 (2014)

    work page 2014

  55. [55]

    C.R.Shalizi,arXive-prints (2007),arXiv:math/0701854 [math.ST]

    work page arXiv 2007

  56. [56]

    K. S. Lomax, Journal of the American Statistical Asso- ciation49, 847 (1954)

    work page 1954

  57. [57]

    Feller,An Introduction to Probability Theory and Its Applications, Volume II, 2nd ed

    W. Feller,An Introduction to Probability Theory and Its Applications, Volume II, 2nd ed. (Wiley, New York, 1971)

    work page 1971

  58. [58]

    Redner,A Guide to First-Passage Processes(Cam- bridge University Press, Cambridge, 2001)

    S. Redner,A Guide to First-Passage Processes(Cam- bridge University Press, Cambridge, 2001). 21

    work page 2001

  59. [59]

    Zaburdaev, S

    V. Zaburdaev, S. Denisov, and J. Klafter, Reviews of Modern Physics87, 483 (2015)

    work page 2015

  60. [60]

    Günaydin and A

    M. Günaydin and A. Kidambi, Fortsch. Phys.72, 2300242 (2024), arXiv:2209.05004 [hep-th]

    work page arXiv 2024

  61. [61]

    Ferrara, R

    S. Ferrara, R. Kallosh, and A. Strominger, Physical Re- view D52, R5412 (1995)

    work page 1995

  62. [62]

    Ferrara, G

    S. Ferrara, G. W. Gibbons, and R. Kallosh, Nuclear Physics B500, 75 (1997)

    work page 1997

  63. [63]

    Ceresole, S

    A. Ceresole, S. Ferrara, and A. Marrani, Classical and Quantum Gravity24, 5651 (2007), arXiv:0707.0964 [hep- th]

    work page arXiv 2007

  64. [64]

    R. D. Schafer,An Introduction to Nonassociative Alge- bras(Academic Press, New York, 1966)

    work page 1966

  65. [65]

    Krutelevich, Journal of Algebra314, 924 (2007)

    S. Krutelevich, Journal of Algebra314, 924 (2007)

    work page 2007

  66. [66]

    Faraut and A

    J. Faraut and A. Korányi,Analysis on Symmetric Cones (Oxford University Press, Oxford, 1994)

    work page 1994

  67. [67]

    Koecher, American Journal of Mathematics79, 575 (1957)

    M. Koecher, American Journal of Mathematics79, 575 (1957)

    work page 1957

  68. [68]

    E. B. Vinberg, Transactions of the Moscow Mathemati- cal Society12, 340 (1963), english translation of Trudy Moskov. Mat. Obshch. 12, 303–358

    work page 1963

  69. [69]

    Bellissard and B

    J. Bellissard and B. Iochum, Annales de l’Institut Fourier 28, 27 (1978)

    work page 1978

  70. [70]

    Hanche-Olsen, Canadian Journal of Mathematics35, 1059 (1983)

    H. Hanche-Olsen, Canadian Journal of Mathematics35, 1059 (1983)

    work page 1983

  71. [71]

    H. P. Petersson, Comm. Algebra32, 1019 (2004)

    work page 2004

  72. [72]

    H. P. Petersson, Transform. Groups24, 219 (2019)

    work page 2019

  73. [73]

    J. C. Baez, Bull. Amer. Math. Soc.39, 145 (2002)

    work page 2002

  74. [74]

    P. M. Cohn, Canadian Journal of Mathematics6, 253 (1954)

    work page 1954

  75. [75]

    Jacobson and L

    N. Jacobson and L. J. Paige, Journal of Mathematics and Mechanics6, 895 (1957)

    work page 1957

  76. [76]

    Barnum, M

    H. Barnum, M. A. Graydon, and A. Wilce, Quantum4, 359 (2020)

    work page 2020

  77. [77]

    Ferrara and R

    S. Ferrara and R. Kallosh, Physical Review D54, 1514 (1996)

    work page 1996

  78. [78]

    Meessen, T

    P. Meessen, T. Ortín, J. Perz, and C. S. Shahbazi, JHEP 2012(9), 001

    work page 2012

  79. [79]

    P. C. Vaidya, Current Science12, 183 (1943)

    work page 1943

  80. [80]

    Nakajima, Progress of Theoretical Physics20, 948 (1958)

    S. Nakajima, Progress of Theoretical Physics20, 948 (1958)

    work page 1958

Showing first 80 references.