References

CCJ

C. G. Callan, Jr., S. Coleman, and R. Jackiw, “A new improved energy-momentum tensor,” Annals of Physics 59 (1970), 42–73. doi:10.1016/0003-4916(70)90394-5.

Nelson

E. Nelson, “Analytic vectors,” Annals of Mathematics 70 (1959), 572–615. doi:10.2307/1970331.

Trotter

H. F. Trotter, “On the product of semi-groups of operators,” Proceedings of the American Mathematical Society 10 (1959), 545–551. doi:10.1090/S0002-9939-1959-0108732-6.

Sanders

K. Sanders, “Essential self-adjointness of Wick squares in quasi-free Hadamard representations on curved spacetimes,” Journal of Mathematical Physics 53 (2012), 042502. arXiv:1010.3978. doi:10.1063/1.3703516.

DutschBoas

M. Dütsch and F.-M. Boas, “The Master Ward Identity,” Reviews in Mathematical Physics 14 (2002), 977–1049. arXiv:hep-th/0111101.

FR

K. Fredenhagen and K. Rejzner, Perturbative algebraic quantum field theory, arXiv:1208.1428. Reference framework for functional products and their domains; no unspecified product theorem is imported.

HislopLongo

P. D. Hislop and R. Longo, “Modular structure of the local algebras associated with the free massless scalar field theory,” Communications in Mathematical Physics 84 (1982), 71–85. doi:10.1007/BF01208372.

BGL

R. Brunetti, D. Guido, and R. Longo, “Modular structure and duality in conformal quantum field theory,” Communications in Mathematical Physics 156 (1993), 201–219. arXiv:funct-an/9302008. doi:10.1007/BF02096738.

DKST

A. Dymarsky, Z. Komargodski, A. Schwimmer, and S. Theisen, “On scale and conformal invariance in four dimensions,” Journal of High Energy Physics 10 (2015), 171. arXiv:1309.2921. doi:10.1007/JHEP10(2015)171.

DFKLP

A. Dymarsky, K. Farnsworth, Z. Komargodski, M. A. Luty, and V. Prilepina, “Scale invariance, conformality, and generalized free fields,” Journal of High Energy Physics 02 (2016), 099. arXiv:1402.6322. doi:10.1007/JHEP02(2016)099.

Baume

F. Baume, B. Keren-Zur, R. Rattazzi, and L. Vitale, “The local Callan–Symanzik equation: structure and applications,” Journal of High Energy Physics 08 (2014), 152. arXiv:1401.5983. doi:10.1007/JHEP08(2014)152.

CheungA

N. Cheung, Oai282-A. Supplied predecessor synopsis, n.d. The full source was not supplied for this continuation. Referenced labels include thm:ward, prop:finitefit, prop:affine-ward, prop:flow, prop:nonintegrable, prop:coverage, and prop:descent. Documentary comparison, not a proof premise.

CheungII

N. Cheung, Landmark II. Supplied synopsis, n.d.; in particular lem:coverage. Documentary comparison for finite contact certificates and spanning-family discipline.

CheungVIIH

N. Cheung, VII-H, version 1. Supplied manuscript excerpts, n.d.; in particular thm:main and its Wick-square susceptibility benchmark. Enter Calculus Companion, https://enter.grok.me. Documentary comparison, not a Ward prescription used here.

CheungIII

N. Cheung, Landmark III. Supplied synopsis, n.d.; prop:Ward and thm:Killing. Classical comparison interface.

CheungV

N. Cheung, Landmark V. Supplied synopsis, n.d.; thm:rawcurrent. Admissible-current comparison interface.

CheungVI

N. Cheung, Landmark VI. Supplied synopsis, n.d.; thm:descent and thm:plateau-obstruction. Classical jet-descent comparison interface.

CheungXIVH

N. Cheung, Landmark XIV-H: Internal kernel relations on the operator route, version 1. Supplied excerpts of XIV-H.tex, n.d.; prop:K5exact, thm:H2, and thm:release. Enter Calculus Companion, https://enter.grok.me.

CheungXIVI

N. Cheung, Landmark XIV-I, version 1. Supplied excerpts of XIV-I.tex, n.d.; prop:pole, thm:I2, thm:I3, and thm:release. Enter Calculus Companion, https://enter.grok.me. Internal amplitude construction; complete joint-map boundary kept separate.

CheungXIVJ

N. Cheung, Landmark XIV-J, version 1. Supplied excerpts of XIV-J.tex, n.d.; prop:descent, lem:null, thm:reference, thm:conditionalextension, thm:J2, and cor:noadmission. Enter Calculus Companion, https://enter.grok.me.

CheungXVB

N. Cheung, Landmark XV-B, version 2. Supplied excerpts of XV-B.tex, n.d.; thm:lifting, thm:contact, thm:jetnull, thm:pointcorrection, and thm:release. Enter Calculus Companion, https://enter.grok.me. Technical descent and extension interfaces; not admission of the inherited full graph.

CheungXVIN

N. Cheung, Landmark XVI-N, version r12. Supplied excerpts of XVI-N.tex, n.d.; thm:massless-obstruction and lem:field-only. Enter Calculus Companion, https://enter.grok.me. Scoped prepared-insertion comparison, not a physical-$L$ theorem.

CheungEm02E

N. Cheung, Em02-E, version 1. Supplied excerpts of Em02-E-v1.tex, n.d.; thm:lapse. Enter Calculus Companion, https://enter.grok.me. Classical relational-lapse comparison.

CheungEm03A

N. Cheung, Em03-A, version 1. Supplied excerpts of Em03-A-v1.tex, n.d.; thm:main. Enter Calculus Companion, https://enter.grok.me. Fixed-background scalar-emission comparison.

CheungEn03A

N. Cheung, En03-A, version 1. Supplied excerpts of En03-A.tex, n.d.; thm:locality. Enter Calculus Companion, https://enter.grok.me. Prescribed-schedule locality comparison.

CheungEn05A

N. Cheung, En05-A, version 1. Supplied excerpts of En05-A.tex, n.d.; thm:cone. Enter Calculus Companion, https://enter.grok.me. Schedule-past and metric-envelope comparison.

CheungEn06A

N. Cheung, En06-A, version 1. Supplied excerpts of En06-A.tex, n.d.; thm:algmicro and its observable-limit hypotheses. Enter Calculus Companion, https://enter.grok.me. Conditional algebraic-microcausality comparison.

CheungEn06B

N. Cheung, En06-B, version 1. Supplied excerpts of En06-B.tex, n.d.; thm:identity. Enter Calculus Companion, https://enter.grok.me. Complete payload-transport comparison.

CheungHawk04A

N. Cheung, Hawk04-A, version 1. Supplied excerpts of Hawk04-A.tex, n.d.; thm:exact. Enter Calculus Companion, https://enter.grok.me. Complete-complement recovery comparison.

Cheung280A

N. Cheung, Oai280-A. Supplied synopsis, n.d.; thm:extensionseparation. Documentary separation of net extensions from metric and radiation-history claims.

OpenAICatalogue

OpenAI, OpenAI manuscript catalogue and Family 282 source record (2026). Supplied record dated October 7, 2026; in particular rem:oai-p-282-01, together with the supplied comparison descriptions of Families 280, 290, 265, 362, and 376. Enter Calculus Companion, https://enter.grok.me. Catalogue records are not independently verified theorem premises.