{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:5VRQL75VGXMZW6MHJFQHMOR6PO","short_pith_number":"pith:5VRQL75V","canonical_record":{"source":{"id":"1703.01071","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-03-03T08:05:33Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"f120888157798d71d899aa42644b460b97df63a25c1eaae5f0cf35414d34bc2f","abstract_canon_sha256":"234478ef83d89889c7852f60e50a72372c7fc3950ed8c91f398ae52965a2afe1"},"schema_version":"1.0"},"canonical_sha256":"ed6305ffb535d99b79874960763a3e7ba25b0f953a4d9b46ba7e613ba76fc776","source":{"kind":"arxiv","id":"1703.01071","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.01071","created_at":"2026-05-18T00:31:00Z"},{"alias_kind":"arxiv_version","alias_value":"1703.01071v2","created_at":"2026-05-18T00:31:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.01071","created_at":"2026-05-18T00:31:00Z"},{"alias_kind":"pith_short_12","alias_value":"5VRQL75VGXMZ","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_16","alias_value":"5VRQL75VGXMZW6MH","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_8","alias_value":"5VRQL75V","created_at":"2026-05-18T12:31:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:5VRQL75VGXMZW6MHJFQHMOR6PO","target":"record","payload":{"canonical_record":{"source":{"id":"1703.01071","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-03-03T08:05:33Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"f120888157798d71d899aa42644b460b97df63a25c1eaae5f0cf35414d34bc2f","abstract_canon_sha256":"234478ef83d89889c7852f60e50a72372c7fc3950ed8c91f398ae52965a2afe1"},"schema_version":"1.0"},"canonical_sha256":"ed6305ffb535d99b79874960763a3e7ba25b0f953a4d9b46ba7e613ba76fc776","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:31:00.104793Z","signature_b64":"dsUE4Z++7HA2/P5nGGpueaKj/FRwwImvjWb6LsgspEru0Isl2sqVAYTCbKgqBHRiBGxNn7+a4Vmh90kBUl6wDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ed6305ffb535d99b79874960763a3e7ba25b0f953a4d9b46ba7e613ba76fc776","last_reissued_at":"2026-05-18T00:31:00.104058Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:31:00.104058Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1703.01071","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":"2026-05-18T00:31:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XNzLT9fTETWPNJ94F5DTFHIMW/K9WS2ov7f/SI3YLCmmnshmudGOwevLmTOWt0vUBnpF0JeJfK8BhP85j605Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T12:10:19.582952Z"},"content_sha256":"d3a52eda8168b345a242bb5e684bbc91afd4c2b26d712114ac28c479fd192702","schema_version":"1.0","event_id":"sha256:d3a52eda8168b345a242bb5e684bbc91afd4c2b26d712114ac28c479fd192702"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:5VRQL75VGXMZW6MHJFQHMOR6PO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A topological proof of the non-degeneracy of harmonic structures on Sierpinski Gaskets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.CA","authors_text":"Hua Qiu, Shiping Cao","submitted_at":"2017-03-03T08:05:33Z","abstract_excerpt":"We present a direct proof of the non-degeneracy of the harmonic structures on the level-$n$ Sierpinski gaskets for any $n\\geq 2$, which was conjectured by Hino in [H1,H2] and confirmed to be true by Tsougkas [T] very recently using Tutte's spring theorem."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.01071","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":"2026-05-18T00:31:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hXGIxrsf9V+HtfWvCD4ac0PYM0HEggQqo3Qhl4DrebQyUUUpgkv4qr9fGH+eqrbocBO1gAVWpA1JxeqpFdYMDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T12:10:19.583491Z"},"content_sha256":"5d592b2d91ea27c4b79e5b25be04d264c8b1b779a2f448c7b80e4ff61608c7d1","schema_version":"1.0","event_id":"sha256:5d592b2d91ea27c4b79e5b25be04d264c8b1b779a2f448c7b80e4ff61608c7d1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5VRQL75VGXMZW6MHJFQHMOR6PO/bundle.json","state_url":"https://pith.science/pith/5VRQL75VGXMZW6MHJFQHMOR6PO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5VRQL75VGXMZW6MHJFQHMOR6PO/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":"2026-05-31T12:10:19Z","links":{"resolver":"https://pith.science/pith/5VRQL75VGXMZW6MHJFQHMOR6PO","bundle":"https://pith.science/pith/5VRQL75VGXMZW6MHJFQHMOR6PO/bundle.json","state":"https://pith.science/pith/5VRQL75VGXMZW6MHJFQHMOR6PO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5VRQL75VGXMZW6MHJFQHMOR6PO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:5VRQL75VGXMZW6MHJFQHMOR6PO","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":"234478ef83d89889c7852f60e50a72372c7fc3950ed8c91f398ae52965a2afe1","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-03-03T08:05:33Z","title_canon_sha256":"f120888157798d71d899aa42644b460b97df63a25c1eaae5f0cf35414d34bc2f"},"schema_version":"1.0","source":{"id":"1703.01071","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.01071","created_at":"2026-05-18T00:31:00Z"},{"alias_kind":"arxiv_version","alias_value":"1703.01071v2","created_at":"2026-05-18T00:31:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.01071","created_at":"2026-05-18T00:31:00Z"},{"alias_kind":"pith_short_12","alias_value":"5VRQL75VGXMZ","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_16","alias_value":"5VRQL75VGXMZW6MH","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_8","alias_value":"5VRQL75V","created_at":"2026-05-18T12:31:00Z"}],"graph_snapshots":[{"event_id":"sha256:5d592b2d91ea27c4b79e5b25be04d264c8b1b779a2f448c7b80e4ff61608c7d1","target":"graph","created_at":"2026-05-18T00:31:00Z","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":"We present a direct proof of the non-degeneracy of the harmonic structures on the level-$n$ Sierpinski gaskets for any $n\\geq 2$, which was conjectured by Hino in [H1,H2] and confirmed to be true by Tsougkas [T] very recently using Tutte's spring theorem.","authors_text":"Hua Qiu, Shiping Cao","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-03-03T08:05:33Z","title":"A topological proof of the non-degeneracy of harmonic structures on Sierpinski Gaskets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.01071","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:d3a52eda8168b345a242bb5e684bbc91afd4c2b26d712114ac28c479fd192702","target":"record","created_at":"2026-05-18T00:31:00Z","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":"234478ef83d89889c7852f60e50a72372c7fc3950ed8c91f398ae52965a2afe1","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-03-03T08:05:33Z","title_canon_sha256":"f120888157798d71d899aa42644b460b97df63a25c1eaae5f0cf35414d34bc2f"},"schema_version":"1.0","source":{"id":"1703.01071","kind":"arxiv","version":2}},"canonical_sha256":"ed6305ffb535d99b79874960763a3e7ba25b0f953a4d9b46ba7e613ba76fc776","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ed6305ffb535d99b79874960763a3e7ba25b0f953a4d9b46ba7e613ba76fc776","first_computed_at":"2026-05-18T00:31:00.104058Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:31:00.104058Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dsUE4Z++7HA2/P5nGGpueaKj/FRwwImvjWb6LsgspEru0Isl2sqVAYTCbKgqBHRiBGxNn7+a4Vmh90kBUl6wDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:31:00.104793Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.01071","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d3a52eda8168b345a242bb5e684bbc91afd4c2b26d712114ac28c479fd192702","sha256:5d592b2d91ea27c4b79e5b25be04d264c8b1b779a2f448c7b80e4ff61608c7d1"],"state_sha256":"14057670200169a392a55dc566eb024746d933681c14ebc11e96c8e75b87b2ac"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Wg/LQ/fN/qaFvUMWI5Y3mZUpacPkrbyA5oh6ZyAz7QmVs2gYW3bnBrFqoKD79oME3J7I3PB5IkDAF5onHVW9BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T12:10:19.586184Z","bundle_sha256":"b086f4b54962ca4597fa65dbed97fbc33b481debb72fbd18856b1325f3367ae5"}}