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Paper Citation Record · LEDGER

From Technical Feasibility to Substitutability: A Geometric Theory of Differentiation

As of 7 August 2026, this Paper Citation Record lists 20 of 20 outbound references and 0 inbound Pith citation observations for arXiv:2507.01985.

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

pith.paper-citation-record.v1
2507.01985 v3

Coverage vector

measured 20 of 20 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-05-22T00:11:28.864683Z

measured 20 of 20 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-06T06:34:29.942622+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

20 of 20 outbound references displayed

  • verified exact1
  • verified fuzzy18
  • unresolved1
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 9cab86fb-92aa-45b7-ad86-629697115f5a · outbound

This paper cites Equilibrium existence in the linear model of spatial competition.

From Technical Feasibility to Substitutability: A Geometric Theory of Differentiation Equilibrium existence in the linear model of spatial competition

Reference 1

Resolution
verified fuzzy
raw_fallback, observed 2026-05-22T00:14:29.622291Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

source=pdf_text observed=2026-05-22T00:11:28.864683Z digest=sha256:7429f5a35469b47230278e8bb80390354952cad0455c6cb3c701181aceb2a417

Observation db59cd69-fb17-4bb8-bd14-6e3eb1527405 · outbound

This paper cites Spatial competition with price-taking firms.

From Technical Feasibility to Substitutability: A Geometric Theory of Differentiation Spatial competition with price-taking firms

Reference 2

Resolution
verified fuzzy
raw_fallback, observed 2026-05-22T00:14:29.618516Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

source=pdf_text observed=2026-05-22T00:11:28.864683Z digest=sha256:f5a9313ad72a41d941ff5c78aecdbd25d523e2630f7f6f77ee3f930fa97c5432

Observation 346900c5-26a4-4def-8d17-9937fafa39b4 · outbound

This paper cites A geometric approach to weakly identified econometric mod- els.

From Technical Feasibility to Substitutability: A Geometric Theory of Differentiation A geometric approach to weakly identified econometric mod- els

Reference 3

Resolution
verified fuzzy
raw_fallback, observed 2026-05-22T00:14:29.614288Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

source=pdf_text observed=2026-05-22T00:11:28.864683Z digest=sha256:953220e2e139a0505c957ce43a9d7e3eccdbeea862e5e1e80dc0697862737b6e

Observation ca926dec-a9f3-4f5b-8263-0807312e1616 · outbound

This paper cites GENERALISING HOTELLING’S LAW: Economic and Philosophical Findings from Agent-Based Modelling.

From Technical Feasibility to Substitutability: A Geometric Theory of Differentiation GENERALISING HOTELLING’S LAW: Economic and Philosophical Findings from Agent-Based Modelling

Reference 4

Resolution
verified fuzzy
raw_fallback, observed 2026-05-22T00:14:29.610567Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

source=pdf_text observed=2026-05-22T00:11:28.864683Z digest=sha256:bc2fc7a27dec1f5b71c5b3015f67b37f5c8dd6ce65196e6552f06f1c22ef7f17

Observation e71dfe07-271d-4d28-b949-41ee9e203fec · outbound

This paper cites Demand functions and demand manifolds.

From Technical Feasibility to Substitutability: A Geometric Theory of Differentiation Demand functions and demand manifolds

Reference 5

Resolution
verified fuzzy
raw_fallback, observed 2026-05-22T00:14:29.607151Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

source=pdf_text observed=2026-05-22T00:11:28.864683Z digest=sha256:082ef4c865fb4e3be6937002e588760c02ba372b6fbd020ad4f9f0e205edc578

Observation 34c96b07-ce4b-4877-9b98-b5e30786d6a5 · outbound

This paper cites Models of spatial competition: A critical review.

From Technical Feasibility to Substitutability: A Geometric Theory of Differentiation Models of spatial competition: A critical review

Reference 6

Resolution
verified fuzzy
raw_fallback, observed 2026-05-22T00:14:29.602928Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

source=pdf_text observed=2026-05-22T00:11:28.864683Z digest=sha256:9850487a3e423e928da804e01d28fa7cd32ecdcdf6c35c46b121eaa601d930b6

Observation 7e605ffa-dff4-4fb9-811b-b5cbbc2395ef · outbound

This paper cites Hotelling’s Minimum Differentiation Principle in a Continuous-Time Experiment with Price and Location Choices.

From Technical Feasibility to Substitutability: A Geometric Theory of Differentiation Hotelling’s Minimum Differentiation Principle in a Continuous-Time Experiment with Price and Location Choices

Reference 7

Resolution
verified fuzzy
raw_fallback, observed 2026-05-22T00:14:29.596942Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

source=pdf_text observed=2026-05-22T00:11:28.864683Z digest=sha256:ae8f279c7877cfea7d8927ded403cdc69a6f150a1265fddae8501aff4438b5c6

Observation 17676d23-66ed-4814-9471-f3c95bf9996f · outbound

This paper cites Hotelling games with three, four, and more players.

From Technical Feasibility to Substitutability: A Geometric Theory of Differentiation Hotelling games with three, four, and more players

Reference 8

Resolution
verified fuzzy
raw_fallback, observed 2026-05-22T00:14:29.560533Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

source=pdf_text observed=2026-05-22T00:11:28.864683Z digest=sha256:be6b269747f50bec6551ff9f9ca775cf01a7560eeedf3ab1cc03f79230f43af9

Observation 52889822-7b8d-4b0a-bcad-9198e3799499 · outbound

This paper cites Aggregation and market demand: an exterior differen- tial calculus viewpoint.

From Technical Feasibility to Substitutability: A Geometric Theory of Differentiation Aggregation and market demand: an exterior differen- tial calculus viewpoint

Reference 9

Resolution
verified fuzzy
raw_fallback, observed 2026-05-22T00:14:29.592000Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

source=pdf_text observed=2026-05-22T00:11:28.864683Z digest=sha256:2bdf1835ee91168900939cf5d0a6a0ce3cfed8123ddbe0967b047f581fcfc6b3

Observation fbc70405-3dca-406a-9a92-9d96745d782d · outbound

This paper cites On Hotelling’s Stability in com- petition.

From Technical Feasibility to Substitutability: A Geometric Theory of Differentiation On Hotelling’s Stability in com- petition

Reference 10

Resolution
verified fuzzy
raw_fallback, observed 2026-05-22T00:14:29.574464Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

source=pdf_text observed=2026-05-22T00:11:28.864683Z digest=sha256:bd1a380358a759bffb3f1badadb9df49c774651c4932197c54977aa0de2bb3d3

Observation 22f7c676-1252-4b4f-9e86-27da3ea095c9 · outbound

This paper cites The principle of minimum differentiation reconsidered: Some new developments in the theory of spatial competition.

From Technical Feasibility to Substitutability: A Geometric Theory of Differentiation The principle of minimum differentiation reconsidered: Some new developments in the theory of spatial competition

Reference 11

Resolution
verified fuzzy
raw_fallback, observed 2026-05-22T00:14:29.564579Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

source=pdf_text observed=2026-05-22T00:11:28.864683Z digest=sha256:6d267c379432b7ec98fbcfd3905886030cd10465dd2dfa6939bee6bb05faa3f6

Observation 61ec84d2-6d57-428d-9008-746de0a56e43 · outbound

This paper cites Where to locate in a circular city?.

From Technical Feasibility to Substitutability: A Geometric Theory of Differentiation Where to locate in a circular city?

Reference 12

Resolution
verified fuzzy
raw_fallback, observed 2026-05-22T00:14:29.557672Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

source=pdf_text observed=2026-05-22T00:11:28.864683Z digest=sha256:476a18f116e0a6c51ce9b832ec5880a14900d6d6b35dda722264ca6f6a1af8cc

Observation 62e7a3d3-cb4e-470e-aaa1-e7c98d46c289 · outbound

This paper cites Survival at the center—the stability of minimum dif- ferentiation.

From Technical Feasibility to Substitutability: A Geometric Theory of Differentiation Survival at the center—the stability of minimum dif- ferentiation

Reference 13

Resolution
verified fuzzy
raw_fallback, observed 2026-05-22T00:14:29.554163Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

source=pdf_text observed=2026-05-22T00:11:28.864683Z digest=sha256:0ec3d05aeef179077065775753f4287be0e22891a9a9d0f2744d3432cf5be617

Observation b3e3c210-eba0-4187-b12d-17ae3bd838b2 · outbound

This paper cites Stability in Competition.

From Technical Feasibility to Substitutability: A Geometric Theory of Differentiation Stability in Competition

Reference 14

Resolution
verified fuzzy
raw_fallback, observed 2026-05-22T00:14:29.550766Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

source=pdf_text observed=2026-05-22T00:11:28.864683Z digest=sha256:af409e593db90086289636eb5c10998cf7e4ae2c86d77041f69f7bd477951825

Observation c3c0038d-a737-4404-9164-c07e3c80dc21 · outbound

This paper cites Competition in multi-characteristics spaces: Hotelling was almost right.

From Technical Feasibility to Substitutability: A Geometric Theory of Differentiation Competition in multi-characteristics spaces: Hotelling was almost right

Reference 15

Resolution
verified fuzzy
raw_fallback, observed 2026-05-22T00:14:29.547615Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

source=pdf_text observed=2026-05-22T00:11:28.864683Z digest=sha256:4656e2116c8cd544b3ea3588640dd5ae63ca717604bf22c742be39aec10595e2

Observation 79130357-663e-43e9-9ce4-2aa9d5cac057 · outbound

This paper cites SPATIAL COMPETITION IN A TWO DIMENSIONAL MARKET.

From Technical Feasibility to Substitutability: A Geometric Theory of Differentiation SPATIAL COMPETITION IN A TWO DIMENSIONAL MARKET

Reference 16

Resolution
verified fuzzy
raw_fallback, observed 2026-05-22T00:14:29.568892Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

source=pdf_text observed=2026-05-22T00:11:28.864683Z digest=sha256:4bb0603ff2ab01d723fd8242f1e15c26a841934fa806a6ea7ba9bbe02a8d9e8a

Observation 6e61065b-2554-4826-886f-f4c34a5a2441 · outbound

This paper cites an unresolved cited work.

From Technical Feasibility to Substitutability: A Geometric Theory of Differentiation Unresolved cited work

Reference 17

Resolution
unresolved
raw_fallback, observed 2026-05-22T00:14:29.544015Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

source=pdf_text observed=2026-05-22T00:11:28.864683Z digest=sha256:6a4cea7031291cf873ce1451fba54b9dcc5096ff94e343f10a98281171a9c506

Observation 26ac4d38-4715-4393-9b31-9ae71d06560e · outbound

This paper cites Differentiation in a Two-Dimensional Market with Endogenous Sequential Entry.

From Technical Feasibility to Substitutability: A Geometric Theory of Differentiation Differentiation in a Two-Dimensional Market with Endogenous Sequential Entry

Reference 18

Resolution
verified exact
arxiv_id, observed 2026-05-22T00:14:28.288822Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

source=pdf_text observed=2026-05-22T00:11:28.864683Z digest=sha256:d7b67ceee895d856b4645efbd6e83e5c39828038376085e570ef2472c9dd34aa

Observation a5ae4f7e-c602-40ba-876c-d7a2b9f71ecb · outbound

This paper cites Monopolistic competition with outside goods.

From Technical Feasibility to Substitutability: A Geometric Theory of Differentiation Monopolistic competition with outside goods

Reference 19

Resolution
verified fuzzy
raw_fallback, observed 2026-05-22T00:14:29.540129Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

source=pdf_text observed=2026-05-22T00:11:28.864683Z digest=sha256:7830dd67842081920a7e1a06734c2adbe76940cd62189016662f75b2800e2ff1

Observation 8d4d225e-ea0d-414d-93f8-42a45206a1fc · outbound

This paper cites Spatial duopoly with triangular markets.

From Technical Feasibility to Substitutability: A Geometric Theory of Differentiation Spatial duopoly with triangular markets

Reference 20

Resolution
verified fuzzy
raw_fallback, observed 2026-05-22T00:14:29.535567Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

source=pdf_text observed=2026-05-22T00:11:28.864683Z digest=sha256:21874d4712294d79f2220dacb645c7aadaeead4cc43e57fbcc9b80c5e3fb9ab1

Pith citing papers

No inbound Pith citation observations are available.