{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:GLQCRRI2YXD4FIHSMPEHXBLS7I","short_pith_number":"pith:GLQCRRI2","canonical_record":{"source":{"id":"2506.06209","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AC","submitted_at":"2025-06-06T16:15:22Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"1d56c3270ba8b58ac188989e70dce6e2a7516d83133a3b7ef2adfec44a90c7ae","abstract_canon_sha256":"e27486f26dab7f3f5cccce784109c587b2bb2dbbd4f529d3c5dfb72082975389"},"schema_version":"1.0"},"canonical_sha256":"32e028c51ac5c7c2a0f263c87b8572fa2225e9f5493d5c417b933d891250fc8f","source":{"kind":"arxiv","id":"2506.06209","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.06209","created_at":"2026-07-05T11:17:27Z"},{"alias_kind":"arxiv_version","alias_value":"2506.06209v1","created_at":"2026-07-05T11:17:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.06209","created_at":"2026-07-05T11:17:27Z"},{"alias_kind":"pith_short_12","alias_value":"GLQCRRI2YXD4","created_at":"2026-07-05T11:17:27Z"},{"alias_kind":"pith_short_16","alias_value":"GLQCRRI2YXD4FIHS","created_at":"2026-07-05T11:17:27Z"},{"alias_kind":"pith_short_8","alias_value":"GLQCRRI2","created_at":"2026-07-05T11:17:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:GLQCRRI2YXD4FIHSMPEHXBLS7I","target":"record","payload":{"canonical_record":{"source":{"id":"2506.06209","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AC","submitted_at":"2025-06-06T16:15:22Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"1d56c3270ba8b58ac188989e70dce6e2a7516d83133a3b7ef2adfec44a90c7ae","abstract_canon_sha256":"e27486f26dab7f3f5cccce784109c587b2bb2dbbd4f529d3c5dfb72082975389"},"schema_version":"1.0"},"canonical_sha256":"32e028c51ac5c7c2a0f263c87b8572fa2225e9f5493d5c417b933d891250fc8f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:17:27.540825Z","signature_b64":"ApTGjC/Ma8aTZJsX+RFYFJIB3V2IlcUKF1QGxaPBvDh5fJu+ITacjMElxqM+9eVWq59MvpCkbVwfa43oJO8oAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"32e028c51ac5c7c2a0f263c87b8572fa2225e9f5493d5c417b933d891250fc8f","last_reissued_at":"2026-07-05T11:17:27.540333Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:17:27.540333Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2506.06209","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:17:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gpT45MQXqYfVt/TCHOeGamgtGaz39rX+AwiOiJk+lYB/0rxyTaTF+biDdq7KovPusTqfd29Ng3ZBjxCW6OsjAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T23:49:53.417766Z"},"content_sha256":"8d180050e79d430935c845672af303bfff0a6dd618013499a796192cd9a92392","schema_version":"1.0","event_id":"sha256:8d180050e79d430935c845672af303bfff0a6dd618013499a796192cd9a92392"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:GLQCRRI2YXD4FIHSMPEHXBLS7I","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Trees whose path ideals have linear quotients","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AC","authors_text":"Animikha Dutta Dhar, Aniruda Suswaram, Kanoy Kumar Das, Pranath S Karanth, Trung Chau","submitted_at":"2025-06-06T16:15:22Z","abstract_excerpt":"For any integer $n$, we classify all trees whose $n$-path ideals have linear quotients."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.06209","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.06209/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T11:17:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"z887+Xkac3K8TyiOLisYxLL+yODjPf9f+enGDdEZCPd5/1kY2+0xPplQD4jzUl5rx0HkDLCjm4a5E/HHw9VmBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T23:49:53.418229Z"},"content_sha256":"57a76dfd2281947b18f87d26638a782420e8c7a62b4ae0e9077f963819c7c251","schema_version":"1.0","event_id":"sha256:57a76dfd2281947b18f87d26638a782420e8c7a62b4ae0e9077f963819c7c251"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GLQCRRI2YXD4FIHSMPEHXBLS7I/bundle.json","state_url":"https://pith.science/pith/GLQCRRI2YXD4FIHSMPEHXBLS7I/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GLQCRRI2YXD4FIHSMPEHXBLS7I/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":"2026-08-07T23:49:53Z","links":{"resolver":"https://pith.science/pith/GLQCRRI2YXD4FIHSMPEHXBLS7I","bundle":"https://pith.science/pith/GLQCRRI2YXD4FIHSMPEHXBLS7I/bundle.json","state":"https://pith.science/pith/GLQCRRI2YXD4FIHSMPEHXBLS7I/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GLQCRRI2YXD4FIHSMPEHXBLS7I/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:GLQCRRI2YXD4FIHSMPEHXBLS7I","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":"e27486f26dab7f3f5cccce784109c587b2bb2dbbd4f529d3c5dfb72082975389","cross_cats_sorted":["math.CO"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AC","submitted_at":"2025-06-06T16:15:22Z","title_canon_sha256":"1d56c3270ba8b58ac188989e70dce6e2a7516d83133a3b7ef2adfec44a90c7ae"},"schema_version":"1.0","source":{"id":"2506.06209","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.06209","created_at":"2026-07-05T11:17:27Z"},{"alias_kind":"arxiv_version","alias_value":"2506.06209v1","created_at":"2026-07-05T11:17:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.06209","created_at":"2026-07-05T11:17:27Z"},{"alias_kind":"pith_short_12","alias_value":"GLQCRRI2YXD4","created_at":"2026-07-05T11:17:27Z"},{"alias_kind":"pith_short_16","alias_value":"GLQCRRI2YXD4FIHS","created_at":"2026-07-05T11:17:27Z"},{"alias_kind":"pith_short_8","alias_value":"GLQCRRI2","created_at":"2026-07-05T11:17:27Z"}],"graph_snapshots":[{"event_id":"sha256:57a76dfd2281947b18f87d26638a782420e8c7a62b4ae0e9077f963819c7c251","target":"graph","created_at":"2026-07-05T11:17:27Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2506.06209/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"For any integer $n$, we classify all trees whose $n$-path ideals have linear quotients.","authors_text":"Animikha Dutta Dhar, Aniruda Suswaram, Kanoy Kumar Das, Pranath S Karanth, Trung Chau","cross_cats":["math.CO"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AC","submitted_at":"2025-06-06T16:15:22Z","title":"Trees whose path ideals have linear quotients"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.06209","kind":"arxiv","version":1},"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":"sha256:8d180050e79d430935c845672af303bfff0a6dd618013499a796192cd9a92392","target":"record","created_at":"2026-07-05T11:17:27Z","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":"e27486f26dab7f3f5cccce784109c587b2bb2dbbd4f529d3c5dfb72082975389","cross_cats_sorted":["math.CO"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AC","submitted_at":"2025-06-06T16:15:22Z","title_canon_sha256":"1d56c3270ba8b58ac188989e70dce6e2a7516d83133a3b7ef2adfec44a90c7ae"},"schema_version":"1.0","source":{"id":"2506.06209","kind":"arxiv","version":1}},"canonical_sha256":"32e028c51ac5c7c2a0f263c87b8572fa2225e9f5493d5c417b933d891250fc8f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"32e028c51ac5c7c2a0f263c87b8572fa2225e9f5493d5c417b933d891250fc8f","first_computed_at":"2026-07-05T11:17:27.540333Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:17:27.540333Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ApTGjC/Ma8aTZJsX+RFYFJIB3V2IlcUKF1QGxaPBvDh5fJu+ITacjMElxqM+9eVWq59MvpCkbVwfa43oJO8oAA==","signature_status":"signed_v1","signed_at":"2026-07-05T11:17:27.540825Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.06209","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8d180050e79d430935c845672af303bfff0a6dd618013499a796192cd9a92392","sha256:57a76dfd2281947b18f87d26638a782420e8c7a62b4ae0e9077f963819c7c251"],"state_sha256":"6155c44e5a8a7ad9ec826b19f1559be563f01d72030bf906882247dbd060efe6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Rtr7FD4PQtcqYGkXH9pwBvTaf1I2x+brid9vol6MYHP+67HhgsLUS5r8tg03lh/GnZcB38fvo/aNdOfBaCD3CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-07T23:49:53.422331Z","bundle_sha256":"bb42f3934dce3b8135069dbe090efa8179e7288d6520915800f6de6fdfc682d9"}}