Paper Citation Record · LEDGER

A Lower Bound for Read-Once Parity Branching Programs

As of 15 August 2026, this Paper Citation Record lists 39 of 39 outbound references and 0 inbound Pith citation observations for arXiv:2607.05944.

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

pith.paper-citation-record.v1
2607.05944 v1

Coverage vector

measured 39 of 39 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-07-08T19:24:43.440406Z

measured 39 of 39 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-14T06:32:32.682623+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: cited_works

Reference resolution

39 of 39 outbound references displayed

verified exact22
verified fuzzy7
unresolved0
parse uncertain0
malformed identifier0
metadata mismatch10

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation acaaf5c1-de18-406b-9b78-befc54e9cfdc · outbound

This paper cites Combinatorica , FJOURNAL =.

A Lower Bound for Read-Once Parity Branching Programs Combinatorica , FJOURNAL =

Reference 1

Resolution: metadata mismatch; doi, observed 2026-07-08T19:25:32.088380Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 7e20fc72-b766-413a-83b4-f95fa9320e75 · outbound

This paper cites http://dx.doi.org/10.1016/0022-0000(87)90010-9 A Lower Bound for Read-Once-Only Branching Programs.

A Lower Bound for Read-Once Parity Branching Programs http://dx.doi.org/10.1016/0022-0000(87)90010-9 A Lower Bound for Read-Once-Only Branching Programs

Reference 2

Resolution: verified exact; doi, observed 2026-07-08T19:25:32.083628Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation cf8441fb-7ec0-4f41-93ef-7134a701b420 · outbound

This paper cites In: Rovan, B., V ojt´aˇa, P.

A Lower Bound for Read-Once Parity Branching Programs In: Rovan, B., V ojt´aˇa, P

Reference 3

Resolution: metadata mismatch; doi, observed 2026-07-08T19:25:32.056055Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 7d75dd89-97ce-42de-9850-8c003926f11b · outbound

This paper cites Razborov, and Roman Smolensky.

A Lower Bound for Read-Once Parity Branching Programs Razborov, and Roman Smolensky

Reference 4

Resolution: verified exact; doi, observed 2026-07-08T19:25:32.060180Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation eb15c718-b4a4-49c8-9453-8d4a2beb1f83 · outbound

This paper cites Theoretical Computer Science , VOLUME =.

A Lower Bound for Read-Once Parity Branching Programs Theoretical Computer Science , VOLUME =

Reference 5

Resolution: metadata mismatch; doi, observed 2026-07-08T19:25:32.062268Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation b3e8e156-cab5-4ff6-b0f0-3959b8e74b1b · outbound

This paper cites http://dx.doi.org/10.1007/S00224-022-10113-9 One-Tape Turing Machine and Branching Program Lower Bounds for MCSP.

A Lower Bound for Read-Once Parity Branching Programs http://dx.doi.org/10.1007/S00224-022-10113-9 One-Tape Turing Machine and Branching Program Lower Bounds for MCSP

Reference 6

Resolution: verified exact; doi, observed 2026-07-08T19:25:32.070014Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation f0b28740-9dcd-43c8-ad47-6acd1dcde01b · outbound

This paper cites http://dx.doi.org/10.4230/LIPICS.CCC.2024.20 Lower Bounds for Set-Multilinear Branching Programs.

A Lower Bound for Read-Once Parity Branching Programs http://dx.doi.org/10.4230/LIPICS.CCC.2024.20 Lower Bounds for Set-Multilinear Branching Programs

Reference 7

Resolution: verified exact; doi, observed 2026-07-08T19:25:32.046170Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 301d4f88-83a2-45df-bf3b-daee30157f1e · outbound

This paper cites http://dx.doi.org/10.1007/S00037-022-00223-8 Quadratic Lower Bounds for Algebraic Branching Programs and Formulas.

A Lower Bound for Read-Once Parity Branching Programs http://dx.doi.org/10.1007/S00037-022-00223-8 Quadratic Lower Bounds for Algebraic Branching Programs and Formulas

Reference 8

Resolution: verified exact; doi, observed 2026-07-08T19:25:32.078699Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 617aa83b-a214-4c9c-8fe3-f7b5fe12ad63 · outbound

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

A Lower Bound for Read-Once Parity Branching Programs Forbes, Mrinal Kumar, and Ramprasad Saptharishi

Reference 9

Resolution: verified exact; doi, observed 2026-07-08T19:25:32.096353Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation a49f1d85-9253-4c85-8bb4-1aae834d6793 · outbound

This paper cites https://eccc.weizmann.ac.il/report/2026/001 Multilinear Algebraic Branching Programs and the Min-Partition Rank Method.

A Lower Bound for Read-Once Parity Branching Programs https://eccc.weizmann.ac.il/report/2026/001 Multilinear Algebraic Branching Programs and the Min-Partition Rank Method

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-07-08T19:25:32.659565Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation a6a368d1-25ac-4aee-8916-a9c68febb46a · outbound

This paper cites an unresolved cited work.

A Lower Bound for Read-Once Parity Branching Programs Unresolved cited work

Reference 11

Resolution: verified exact; doi, observed 2026-07-08T19:25:32.080245Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 662b6c98-35b4-4e88-8b9b-e323224d846f · outbound

This paper cites Forbes and Amir Shpilka , title =.

A Lower Bound for Read-Once Parity Branching Programs Forbes and Amir Shpilka , title =

Reference 12

Resolution: verified exact; doi, observed 2026-07-08T19:25:32.057955Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation e9eba4b4-7ef4-4917-bdf2-a34180eb134b · outbound

This paper cites Forbes and Amir Shpilka and Iddo Tzameret and Avi Wigderson , title =.

A Lower Bound for Read-Once Parity Branching Programs Forbes and Amir Shpilka and Iddo Tzameret and Avi Wigderson , title =

Reference 13

Resolution: verified exact; doi, observed 2026-07-08T19:25:32.053960Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 07d8eb49-b671-485b-b3e6-383d0d7f94c1 · outbound

This paper cites title =.

A Lower Bound for Read-Once Parity Branching Programs title =

Reference 14

Resolution: verified exact; doi, observed 2026-07-08T19:25:32.090326Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 07fad2b0-2f72-4bb6-a201-467eac54b5b0 · outbound

This paper cites On Approximability of Satisfiable k-CSPs: IV , year =.

A Lower Bound for Read-Once Parity Branching Programs On Approximability of Satisfiable k-CSPs: IV , year =

Reference 15

Resolution: metadata mismatch; arxiv_id, observed 2026-07-08T19:25:32.065178Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation a8317add-f392-491d-bcb5-f11a8c96fa84 · outbound

This paper cites http://dx.doi.org/10.1016/J.TCS.2006.01.052 Lower bounds for restricted read-once parity branching programs.

A Lower Bound for Read-Once Parity Branching Programs http://dx.doi.org/10.1016/J.TCS.2006.01.052 Lower bounds for restricted read-once parity branching programs

Reference 16

Resolution: verified exact; doi, observed 2026-07-08T19:25:32.075361Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation a757ec04-11be-400f-a828-59cda3a0a2c8 · outbound

This paper cites http://dx.doi.org/10.1145/322326.322341 Some Exact Complexity Results for Straight-Line Computations over Semirings.

A Lower Bound for Read-Once Parity Branching Programs http://dx.doi.org/10.1145/322326.322341 Some Exact Complexity Results for Straight-Line Computations over Semirings

Reference 17

Resolution: verified exact; arxiv_id, observed 2026-07-08T19:25:32.051555Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation c22c650f-52f7-4e80-a36d-9bbbb485d6c2 · outbound

This paper cites Boolean Function Complexity - Advances and Frontiers , volume 27 of Algorithms and combinatorics.

A Lower Bound for Read-Once Parity Branching Programs Boolean Function Complexity - Advances and Frontiers , volume 27 of Algorithms and combinatorics

Reference 18

Resolution: verified exact; doi, observed 2026-07-08T19:25:32.081983Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation d57ecb6f-f525-4a48-97d7-e9a05fd013da · outbound

This paper cites TITLE =.

A Lower Bound for Read-Once Parity Branching Programs TITLE =

Reference 19

Resolution: metadata mismatch; doi, observed 2026-07-08T19:25:32.039872Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation f2b73ea1-c240-4bb9-91a5-762106635614 · outbound

This paper cites On Span Programs.

A Lower Bound for Read-Once Parity Branching Programs On Span Programs

Reference 20

Resolution: verified exact; arxiv_id, observed 2026-07-08T19:25:32.027884Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 8f32ee0c-6c61-4659-ae3d-e60630756630 · outbound

This paper cites https://www.cse.iitb.ac.in/ nutan/papers/abp-complexity.pdf Homogeneous ABP complexity of elementary symmetric polynomial , 2019.

A Lower Bound for Read-Once Parity Branching Programs https://www.cse.iitb.ac.in/ nutan/papers/abp-complexity.pdf Homogeneous ABP complexity of elementary symmetric polynomial , 2019

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-07-08T19:25:32.662972Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 0aa8dea8-2410-4dea-abcd-6782e6de0b75 · outbound

This paper cites http://dx.doi.org/10.1145/3734215 Superpolynomial Lower Bounds Against Low-Depth Algebraic Circuits.

A Lower Bound for Read-Once Parity Branching Programs http://dx.doi.org/10.1145/3734215 Superpolynomial Lower Bounds Against Low-Depth Algebraic Circuits

Reference 22

Resolution: verified exact; doi, observed 2026-07-08T19:25:32.033239Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 0d58a791-6526-4a19-9131-8f998160c5ee · outbound

This paper cites https://mathoverflow.net/questions/264226/singular-locus-of-zero-set-of-elementary-symmetric-polynomial Singular locus of zero locus of elementary symmetric polynomials , 2017.

A Lower Bound for Read-Once Parity Branching Programs https://mathoverflow.net/questions/264226/singular-locus-of-zero-set-of-elementary-symmetric-polynomial Singular locus of zero locus of elementary symmetric polynomials , 2017

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-07-08T19:25:32.656167Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 210c4935-c50b-4144-857b-c3e17291ec4f · outbound

This paper cites http://mi.mathnet.ru/dan32449 On a Boolean function.

A Lower Bound for Read-Once Parity Branching Programs http://mi.mathnet.ru/dan32449 On a Boolean function

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-07-08T19:25:32.657876Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation b103eb24-2545-4a43-9e21-d66cc33334af · outbound

This paper cites http://dx.doi.org/10.1145/103418.103462 Lower Bounds for Non-Commutative Computation (Extended Abstract).

A Lower Bound for Read-Once Parity Branching Programs http://dx.doi.org/10.1145/103418.103462 Lower Bounds for Non-Commutative Computation (Extended Abstract)

Reference 25

Resolution: verified exact; arxiv_id, observed 2026-07-08T19:25:32.043139Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation e5ba3cf7-fe55-4870-ab0d-e159877a4aa2 · outbound

This paper cites Okolnishnikova.

A Lower Bound for Read-Once Parity Branching Programs Okolnishnikova

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-07-08T19:25:32.661157Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 36f157f7-5a4a-441d-bcb9-039c7b7f0128 · outbound

This paper cites https://eccc.weizmann.ac.il/report/2025/128 Computing the Elementary Symmetric Polynomials in Positive Characteristics.

A Lower Bound for Read-Once Parity Branching Programs https://eccc.weizmann.ac.il/report/2025/128 Computing the Elementary Symmetric Polynomials in Positive Characteristics

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-07-08T19:25:32.664716Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 345c3a28-2422-4ee5-b147-1d83a6937ce4 · outbound

This paper cites Theory Comput.

A Lower Bound for Read-Once Parity Branching Programs Theory Comput

Reference 28

Resolution: metadata mismatch; doi, observed 2026-07-08T19:25:32.092279Z

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No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation ed53c52a-0eb2-44d1-b61f-822573037cef · outbound

This paper cites Vazirani.

A Lower Bound for Read-Once Parity Branching Programs Vazirani

Reference 29

Resolution: metadata mismatch; arxiv_id, observed 2026-07-08T19:25:32.068220Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation de5f274a-6339-4a03-b8a4-60adda4ad800 · outbound

This paper cites http://dx.doi.org/10.1137/070707932 A Lower Bound for the Size of Syntactically Multilinear Arithmetic Circuits.

A Lower Bound for Read-Once Parity Branching Programs http://dx.doi.org/10.1137/070707932 A Lower Bound for the Size of Syntactically Multilinear Arithmetic Circuits

Reference 30

Resolution: verified exact; doi, observed 2026-07-08T19:25:32.048389Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation b78c352e-5991-4559-9436-712541e707e3 · outbound

This paper cites volume = 17, number = 4, pages =.

A Lower Bound for Read-Once Parity Branching Programs volume = 17, number = 4, pages =

Reference 31

Resolution: metadata mismatch; doi, observed 2026-07-08T19:25:32.073629Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 7360c9a1-d508-4514-bc0f-f866c39210bd · outbound

This paper cites Computational Complexity , VOLUME =.

A Lower Bound for Read-Once Parity Branching Programs Computational Complexity , VOLUME =

Reference 32

Resolution: metadata mismatch; doi, observed 2026-07-08T19:25:32.077073Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation d464bc4a-fe6d-42e9-a800-895cd7a3da92 · outbound

This paper cites https://github.com/dasarpmar/lowerbounds-survey/releases/ A survey of lower bounds in arithmetic circuit complexity.

A Lower Bound for Read-Once Parity Branching Programs https://github.com/dasarpmar/lowerbounds-survey/releases/ A survey of lower bounds in arithmetic circuit complexity

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-07-08T19:25:32.654303Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 175338af-f760-43a1-8042-f4f6c3448696 · outbound

This paper cites http://dx.doi.org/10.1016/J.TCS.2005.03.016 A hierarchy result for read-once branching programs with restricted parity nondeterminism.

A Lower Bound for Read-Once Parity Branching Programs http://dx.doi.org/10.1016/J.TCS.2005.03.016 A hierarchy result for read-once branching programs with restricted parity nondeterminism

Reference 34

Resolution: verified exact; doi, observed 2026-07-08T19:25:32.094340Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 160cd0b6-3ad6-498a-8a85-c8815bca41ed · outbound

This paper cites Numerische Mathematik , VOLUME =.

A Lower Bound for Read-Once Parity Branching Programs Numerische Mathematik , VOLUME =

Reference 35

Resolution: metadata mismatch; doi, observed 2026-07-08T19:25:32.071791Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 8dbe7f75-2154-4efb-99ca-f143e140fc77 · outbound

This paper cites http://dx.doi.org/10.1561/0400000039 Arithmetic Circuits: A survey of recent results and open questions.

A Lower Bound for Read-Once Parity Branching Programs http://dx.doi.org/10.1561/0400000039 Arithmetic Circuits: A survey of recent results and open questions

Reference 36

Resolution: verified exact; doi, observed 2026-07-08T19:25:32.035606Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 57c1fa73-911b-4469-8ac2-6624ed111b41 · outbound

This paper cites Thathachar.

A Lower Bound for Read-Once Parity Branching Programs Thathachar

Reference 37

Resolution: verified exact; arxiv_id, observed 2026-07-08T19:25:32.086170Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 8472ed64-c181-4585-b9fd-d7bf107e4902 · outbound

This paper cites http://dx.doi.org/10.1145/42282.46161 On the complexity of branching programs and decision trees for clique functions.

A Lower Bound for Read-Once Parity Branching Programs http://dx.doi.org/10.1145/42282.46161 On the complexity of branching programs and decision trees for clique functions

Reference 38

Resolution: verified exact; arxiv_id, observed 2026-07-08T19:25:32.099169Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 1b7dc0c5-0f98-4934-91fc-1edf1bca5763 · outbound

This paper cites http://dx.doi.org/10.1007/BFB0030340 An Exponential Lower Bound for One-Time-Only Branching Programs.

A Lower Bound for Read-Once Parity Branching Programs http://dx.doi.org/10.1007/BFB0030340 An Exponential Lower Bound for One-Time-Only Branching Programs

Reference 39

Resolution: verified exact; doi, observed 2026-07-08T19:25:32.037708Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Pith citing papers

No inbound Pith citation observations are available.