Paper Citation Record · LEDGER

Functional Lower Bounds in Algebraic Proofs: Symmetry, Lifting, and Barriers

As of 22 August 2026, this Paper Citation Record lists 50 of 50 outbound references and 0 inbound Pith citation observations for arXiv:2412.20114.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2412.20114 v1

Coverage vector

measured 50 of 50 reference resolution

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Pith citing papers itemized under the disclosed page cap.

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Reference resolution

50 of 50 outbound references displayed

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Outbound references

Observation ea4f01f3-8f89-4f29-ac2e-73c712de8d50 · outbound

This paper cites an unresolved cited work.

Functional Lower Bounds in Algebraic Proofs: Symmetry, Lifting, and Barriers Unresolved cited work

Reference 1

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This paper cites Low-Depth Arithmetic Circuit Lower Bounds: Bypassing Set-Multilinearization.

Functional Lower Bounds in Algebraic Proofs: Symmetry, Lifting, and Barriers Low-Depth Arithmetic Circuit Lower Bounds: Bypassing Set-Multilinearization

Reference 3

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Functional Lower Bounds in Algebraic Proofs: Symmetry, Lifting, and Barriers The complexity of the pigeonhole principle

Reference 4

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This paper cites A Lower Bound for Polynomial Calculus with Extension Rule.

Functional Lower Bounds in Algebraic Proofs: Symmetry, Lifting, and Barriers A Lower Bound for Polynomial Calculus with Extension Rule

Reference 5

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This paper cites Lower bounds on H ilbert's N ullstellensatz and propositional proofs.

Functional Lower Bounds in Algebraic Proofs: Symmetry, Lifting, and Barriers Lower bounds on H ilbert's N ullstellensatz and propositional proofs

Reference 6

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This paper cites Buss, Russell Impagliazzo, Jan Kraj \' c ek, Pavel Pudl \' a k, Alexander A.

Functional Lower Bounds in Algebraic Proofs: Symmetry, Lifting, and Barriers Buss, Russell Impagliazzo, Jan Kraj \' c ek, Pavel Pudl \' a k, Alexander A

Reference 7

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This paper cites Lower bounds for cutting planes proofs with small coefficients.

Functional Lower Bounds in Algebraic Proofs: Symmetry, Lifting, and Barriers Lower bounds for cutting planes proofs with small coefficients

Reference 8

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This paper cites Campbell and I.P.

Functional Lower Bounds in Algebraic Proofs: Symmetry, Lifting, and Barriers Campbell and I.P

Reference 9

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This paper cites Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra.

Functional Lower Bounds in Algebraic Proofs: Symmetry, Lifting, and Barriers Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra

Reference 10

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This paper cites Computational Invariant Theory , volume 130 of Encyclopaedia of Mathematical Sciences.

Functional Lower Bounds in Algebraic Proofs: Symmetry, Lifting, and Barriers Computational Invariant Theory , volume 130 of Encyclopaedia of Mathematical Sciences

Reference 11

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This paper cites New lower bounds for polynomial calculus over non-boolean bases.

Functional Lower Bounds in Algebraic Proofs: Symmetry, Lifting, and Barriers New lower bounds for polynomial calculus over non-boolean bases

Reference 12

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Observation 5488ebf2-3a71-4d79-82b3-e5d5c735d099 · outbound

This paper cites de Rezende, Mika G \" o \" o s, and Robert Robere.

Functional Lower Bounds in Algebraic Proofs: Symmetry, Lifting, and Barriers de Rezende, Mika G \" o \" o s, and Robert Robere

Reference 13

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Observation 29cb15f9-812d-48d9-a174-ca4b5c934e34 · outbound

This paper cites Forbes, Mrinal Kumar, and Ramprasad Saptharishi.

Functional Lower Bounds in Algebraic Proofs: Symmetry, Lifting, and Barriers Forbes, Mrinal Kumar, and Ramprasad Saptharishi

Reference 14

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Functional Lower Bounds in Algebraic Proofs: Symmetry, Lifting, and Barriers Unresolved cited work

Reference 15

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Observation 041765a2-9ff8-441e-bce8-df8f14cb1c57 · outbound

This paper cites Forbes and Amir Shpilka.

Functional Lower Bounds in Algebraic Proofs: Symmetry, Lifting, and Barriers Forbes and Amir Shpilka

Reference 16

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Functional Lower Bounds in Algebraic Proofs: Symmetry, Lifting, and Barriers Forbes, Amir Shpilka, Iddo Tzameret, and Avi Wigderson

Reference 17

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Functional Lower Bounds in Algebraic Proofs: Symmetry, Lifting, and Barriers Unresolved cited work

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Functional Lower Bounds in Algebraic Proofs: Symmetry, Lifting, and Barriers Simple hard instances for low-depth algebraic proofs

Reference 19

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Functional Lower Bounds in Algebraic Proofs: Symmetry, Lifting, and Barriers Learning sums of powers of low-degree polynomials in the non-degenerate case

Reference 20

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Functional Lower Bounds in Algebraic Proofs: Symmetry, Lifting, and Barriers Grochow and Toniann Pitassi

Reference 21

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Functional Lower Bounds in Algebraic Proofs: Symmetry, Lifting, and Barriers T seitin's tautologies and lower bounds for N ullstellensatz proofs

Reference 22

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This paper cites Polynomial Identity Testing and the Ideal Proof System: PIT is in NP if and only if IPS can be p-simulated by a Cook-Reckhow proof system.

Functional Lower Bounds in Algebraic Proofs: Symmetry, Lifting, and Barriers Polynomial Identity Testing and the Ideal Proof System: PIT is in NP if and only if IPS can be p-simulated by a Cook-Reckhow proof system

Reference 23

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This paper cites Lower Bounds for Polynomial Calculus with Extension Variables over Finite Fields.

Functional Lower Bounds in Algebraic Proofs: Symmetry, Lifting, and Barriers Lower Bounds for Polynomial Calculus with Extension Variables over Finite Fields

Reference 24

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Functional Lower Bounds in Algebraic Proofs: Symmetry, Lifting, and Barriers Lower bounds for the polynomial calculus and the G r \" o bner basis algorithm

Reference 25

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This paper cites IPS -like proof systems based on binary decision diagrams.

Functional Lower Bounds in Algebraic Proofs: Symmetry, Lifting, and Barriers IPS -like proof systems based on binary decision diagrams

Reference 26

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Observation 3bd9c53e-59a2-455c-84cc-446a8c341893 · outbound

This paper cites An exponential lower bound to the size of bounded depth F rege proofs of the pigeonhole principle.

Functional Lower Bounds in Algebraic Proofs: Symmetry, Lifting, and Barriers An exponential lower bound to the size of bounded depth F rege proofs of the pigeonhole principle

Reference 27

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Functional Lower Bounds in Algebraic Proofs: Symmetry, Lifting, and Barriers Interpolation theorems, lower bounds for proof systems, and independence results for bounded arithmetic

Reference 28

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Functional Lower Bounds in Algebraic Proofs: Symmetry, Lifting, and Barriers Superpolynomial lower bounds against low-depth algebraic circuits

Reference 29

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This paper cites Characterizing Propositional Proofs as Non-Commutative Formulas.

Functional Lower Bounds in Algebraic Proofs: Symmetry, Lifting, and Barriers Characterizing Propositional Proofs as Non-Commutative Formulas

Reference 30

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Functional Lower Bounds in Algebraic Proofs: Symmetry, Lifting, and Barriers Lower bounds for non-commutative computation

Reference 31

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Functional Lower Bounds in Algebraic Proofs: Symmetry, Lifting, and Barriers Exponential lower bounds for the pigeonhole principle

Reference 32

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Functional Lower Bounds in Algebraic Proofs: Symmetry, Lifting, and Barriers Algebraic propositional proof systems

Reference 33

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Functional Lower Bounds in Algebraic Proofs: Symmetry, Lifting, and Barriers Unsolvable systems of equations and proof complexity

Reference 34

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Functional Lower Bounds in Algebraic Proofs: Symmetry, Lifting, and Barriers Algebraic proof complexity: Progress, frontiers and challenges

Reference 35

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This paper cites Razborov.

Functional Lower Bounds in Algebraic Proofs: Symmetry, Lifting, and Barriers Razborov

Reference 36

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Functional Lower Bounds in Algebraic Proofs: Symmetry, Lifting, and Barriers Separation of multilinear circuit and formula size

Reference 37

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This paper cites Multi-linear formulas for permanent and determinant are of super-polynomial size.

Functional Lower Bounds in Algebraic Proofs: Symmetry, Lifting, and Barriers Multi-linear formulas for permanent and determinant are of super-polynomial size

Reference 38

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Functional Lower Bounds in Algebraic Proofs: Symmetry, Lifting, and Barriers On vector invariants over finite fields

Reference 39

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Functional Lower Bounds in Algebraic Proofs: Symmetry, Lifting, and Barriers Resolution over linear equations and multilinear proofs

Reference 40

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Functional Lower Bounds in Algebraic Proofs: Symmetry, Lifting, and Barriers The strength of multilinear proofs

Reference 41

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Functional Lower Bounds in Algebraic Proofs: Symmetry, Lifting, and Barriers Balancing syntactically multilinear arithmetic circuits

Reference 42

Resolution: unresolved; no resolver link, observed 2026-08-10T23:46:56.390738Z

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Functional Lower Bounds in Algebraic Proofs: Symmetry, Lifting, and Barriers Lower bounds and separations for constant depth multilinear circuits

Reference 43

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This paper cites Personal communication to Forbes-Shpilka ForbesShpilka13b.

Functional Lower Bounds in Algebraic Proofs: Symmetry, Lifting, and Barriers Personal communication to Forbes-Shpilka ForbesShpilka13b

Reference 44

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This paper cites A survey of lower bounds in arithmetic circuit complexity, 2016-2022.

Functional Lower Bounds in Algebraic Proofs: Symmetry, Lifting, and Barriers A survey of lower bounds in arithmetic circuit complexity, 2016-2022

Reference 45

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:46:59.533536Z

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Observation 2f5e5fbc-4097-4718-9562-c87e15e302d9 · outbound

This paper cites Diagonal circuit identity testing and lower bounds.

Functional Lower Bounds in Algebraic Proofs: Symmetry, Lifting, and Barriers Diagonal circuit identity testing and lower bounds

Reference 46

Resolution: verified exact; doi, observed 2026-08-10T23:46:56.655666Z

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Observation afc292b6-762f-47b6-9d9b-e7309c30115b · outbound

This paper cites (semi)algebraic proofs over \( \) 1 variables.

Functional Lower Bounds in Algebraic Proofs: Symmetry, Lifting, and Barriers (semi)algebraic proofs over \( \) 1 variables

Reference 47

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This paper cites Iterated lower bound formulas: a diagonalization-based approach to proof complexity.

Functional Lower Bounds in Algebraic Proofs: Symmetry, Lifting, and Barriers Iterated lower bound formulas: a diagonalization-based approach to proof complexity

Reference 48

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Functional Lower Bounds in Algebraic Proofs: Symmetry, Lifting, and Barriers Depth-3 arithmetic circuits over fields of characteristic zero

Reference 49

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:46:59.474904Z

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Observation d395dcde-e926-4aef-b947-669dd2bf4dca · outbound

This paper cites Arithmetic circuits: A survey of recent results and open questions.

Functional Lower Bounds in Algebraic Proofs: Symmetry, Lifting, and Barriers Arithmetic circuits: A survey of recent results and open questions

Reference 50

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:46:59.427557Z

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Observation 831b45a0-6b55-42a9-8d35-d0994bc24c77 · outbound

This paper cites Algebraic proofs over noncommutative formulas.

Functional Lower Bounds in Algebraic Proofs: Symmetry, Lifting, and Barriers Algebraic proofs over noncommutative formulas

Reference 51

Resolution: verified exact; doi, observed 2026-08-10T23:46:56.595252Z

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Pith citing papers

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