{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:EQNFG4LSTY7BJVQGF5B2SN5TPV","short_pith_number":"pith:EQNFG4LS","canonical_record":{"source":{"id":"1712.05449","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-12-14T20:44:19Z","cross_cats_sorted":["math.DS","math.MP"],"title_canon_sha256":"37b8a6050d1eb11e1d8787fa30c65d3eb7da9bab6308bff18ac1e0829990d206","abstract_canon_sha256":"3438e5da57b0c2a05dfefb77352484623f9accc9a18e80dd7548853ba3948fe4"},"schema_version":"1.0"},"canonical_sha256":"241a5371729e3e14d6062f43a937b37d720ff2e7bee696bdf00ae04741826784","source":{"kind":"arxiv","id":"1712.05449","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.05449","created_at":"2026-05-17T23:56:30Z"},{"alias_kind":"arxiv_version","alias_value":"1712.05449v2","created_at":"2026-05-17T23:56:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.05449","created_at":"2026-05-17T23:56:30Z"},{"alias_kind":"pith_short_12","alias_value":"EQNFG4LSTY7B","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"EQNFG4LSTY7BJVQG","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"EQNFG4LS","created_at":"2026-05-18T12:31:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:EQNFG4LSTY7BJVQGF5B2SN5TPV","target":"record","payload":{"canonical_record":{"source":{"id":"1712.05449","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-12-14T20:44:19Z","cross_cats_sorted":["math.DS","math.MP"],"title_canon_sha256":"37b8a6050d1eb11e1d8787fa30c65d3eb7da9bab6308bff18ac1e0829990d206","abstract_canon_sha256":"3438e5da57b0c2a05dfefb77352484623f9accc9a18e80dd7548853ba3948fe4"},"schema_version":"1.0"},"canonical_sha256":"241a5371729e3e14d6062f43a937b37d720ff2e7bee696bdf00ae04741826784","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:56:30.094603Z","signature_b64":"mgSVqw9O9W8URPtLJmFPkdg5sMRe2BfXe4VZZ/oiti3fidfHTCNJjS+jSfGyxMrURTr/g4egNaMlAunbOmVeBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"241a5371729e3e14d6062f43a937b37d720ff2e7bee696bdf00ae04741826784","last_reissued_at":"2026-05-17T23:56:30.094194Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:56:30.094194Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1712.05449","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:56:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EacPC4jro6PVwiPzQzIh4JJ+bkhiG3tI5ALhi5seOK64+Cu6SS3vLxvPjI0/FXN5hppyclU8YZjeNOUzSfVNAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T03:23:38.303641Z"},"content_sha256":"73799bcdc85d171fb6a758340ffbca130563c79a91b192ba59413271eb75da33","schema_version":"1.0","event_id":"sha256:73799bcdc85d171fb6a758340ffbca130563c79a91b192ba59413271eb75da33"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:EQNFG4LSTY7BJVQGF5B2SN5TPV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hilbert's \"monkey saddle\" and other curiosities in the equilibrium problem of three point particles on a circle for repulsive power law forces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.MP"],"primary_cat":"math-ph","authors_text":"Michael K.-H. Kiessling, Renna Yi","submitted_at":"2017-12-14T20:44:19Z","abstract_excerpt":"This article determines all possible equilibrium arrangements (proper as well as pseudo) under repulsive power law forces of three point particles on the unit circle. These are the critical points of the sum over the three (standardized) Riesz pair interaction terms, each given by $V_s(r)= s^{-1}\\left(r^{-s}-1 \\right)$ when the real parameter $s \\neq 0$, and by $V_0(r) := \\lim_{s\\to0}V_s(r) = -\\ln r$; here, $r$ is the chordal distance between the particles in the pair. The bifurcation diagram which exhibits all these equilibrium arrangements together as functions of $s$ features three obvious "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.05449","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:56:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wPDsEuLAs6uroHCilG2uWDw7G/94V0K2T5+xZVtpDPmllXcaFdZYH702Sor5KzHBQ9Df/QiIjTayEkPDWV+xCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T03:23:38.303990Z"},"content_sha256":"e8321d8ff256657808007c0d47bfcd8745acdf8fc79721b1ca2fa1f736b18d30","schema_version":"1.0","event_id":"sha256:e8321d8ff256657808007c0d47bfcd8745acdf8fc79721b1ca2fa1f736b18d30"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EQNFG4LSTY7BJVQGF5B2SN5TPV/bundle.json","state_url":"https://pith.science/pith/EQNFG4LSTY7BJVQGF5B2SN5TPV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EQNFG4LSTY7BJVQGF5B2SN5TPV/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-07-01T03:23:38Z","links":{"resolver":"https://pith.science/pith/EQNFG4LSTY7BJVQGF5B2SN5TPV","bundle":"https://pith.science/pith/EQNFG4LSTY7BJVQGF5B2SN5TPV/bundle.json","state":"https://pith.science/pith/EQNFG4LSTY7BJVQGF5B2SN5TPV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EQNFG4LSTY7BJVQGF5B2SN5TPV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:EQNFG4LSTY7BJVQGF5B2SN5TPV","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"3438e5da57b0c2a05dfefb77352484623f9accc9a18e80dd7548853ba3948fe4","cross_cats_sorted":["math.DS","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-12-14T20:44:19Z","title_canon_sha256":"37b8a6050d1eb11e1d8787fa30c65d3eb7da9bab6308bff18ac1e0829990d206"},"schema_version":"1.0","source":{"id":"1712.05449","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.05449","created_at":"2026-05-17T23:56:30Z"},{"alias_kind":"arxiv_version","alias_value":"1712.05449v2","created_at":"2026-05-17T23:56:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.05449","created_at":"2026-05-17T23:56:30Z"},{"alias_kind":"pith_short_12","alias_value":"EQNFG4LSTY7B","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"EQNFG4LSTY7BJVQG","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"EQNFG4LS","created_at":"2026-05-18T12:31:12Z"}],"graph_snapshots":[{"event_id":"sha256:e8321d8ff256657808007c0d47bfcd8745acdf8fc79721b1ca2fa1f736b18d30","target":"graph","created_at":"2026-05-17T23:56:30Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"This article determines all possible equilibrium arrangements (proper as well as pseudo) under repulsive power law forces of three point particles on the unit circle. These are the critical points of the sum over the three (standardized) Riesz pair interaction terms, each given by $V_s(r)= s^{-1}\\left(r^{-s}-1 \\right)$ when the real parameter $s \\neq 0$, and by $V_0(r) := \\lim_{s\\to0}V_s(r) = -\\ln r$; here, $r$ is the chordal distance between the particles in the pair. The bifurcation diagram which exhibits all these equilibrium arrangements together as functions of $s$ features three obvious ","authors_text":"Michael K.-H. Kiessling, Renna Yi","cross_cats":["math.DS","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-12-14T20:44:19Z","title":"Hilbert's \"monkey saddle\" and other curiosities in the equilibrium problem of three point particles on a circle for repulsive power law forces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.05449","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:73799bcdc85d171fb6a758340ffbca130563c79a91b192ba59413271eb75da33","target":"record","created_at":"2026-05-17T23:56:30Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"3438e5da57b0c2a05dfefb77352484623f9accc9a18e80dd7548853ba3948fe4","cross_cats_sorted":["math.DS","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-12-14T20:44:19Z","title_canon_sha256":"37b8a6050d1eb11e1d8787fa30c65d3eb7da9bab6308bff18ac1e0829990d206"},"schema_version":"1.0","source":{"id":"1712.05449","kind":"arxiv","version":2}},"canonical_sha256":"241a5371729e3e14d6062f43a937b37d720ff2e7bee696bdf00ae04741826784","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"241a5371729e3e14d6062f43a937b37d720ff2e7bee696bdf00ae04741826784","first_computed_at":"2026-05-17T23:56:30.094194Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:56:30.094194Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mgSVqw9O9W8URPtLJmFPkdg5sMRe2BfXe4VZZ/oiti3fidfHTCNJjS+jSfGyxMrURTr/g4egNaMlAunbOmVeBQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:56:30.094603Z","signed_message":"canonical_sha256_bytes"},"source_id":"1712.05449","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:73799bcdc85d171fb6a758340ffbca130563c79a91b192ba59413271eb75da33","sha256:e8321d8ff256657808007c0d47bfcd8745acdf8fc79721b1ca2fa1f736b18d30"],"state_sha256":"f5dbc6a9ba7d09912f06996f2a8a5ea08cc3cfb9a54178def892728a2c12f702"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NUdFyYEME9GjwtpdCvdERnFxMNK11j2fI4qyqYbVaQEP/TgSVH/znd/z9jTkIxb7TDuk5gfi93+Z+spScP3zAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-01T03:23:38.306016Z","bundle_sha256":"772b09ac5bdc9f3d17131ce20b3c7bbb75d27b7d99c85578e3888073d0865939"}}