{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:3FHMFQOGA2L35DDV6AZR7DMKG2","short_pith_number":"pith:3FHMFQOG","canonical_record":{"source":{"id":"0707.0845","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.AG","submitted_at":"2007-07-05T18:01:04Z","cross_cats_sorted":[],"title_canon_sha256":"469de84a42e7bcc3e22c92b92e4217e05b9d4a44d0d0d8d224277052932d40ea","abstract_canon_sha256":"e78539493516272266049da63c334eb3775e826c78ef571324cf1ace97d90c7f"},"schema_version":"1.0"},"canonical_sha256":"d94ec2c1c60697be8c75f0331f8d8a36b7ce9eb9444fba1ae7aed6f8bc5c206a","source":{"kind":"arxiv","id":"0707.0845","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0707.0845","created_at":"2026-05-18T00:05:09Z"},{"alias_kind":"arxiv_version","alias_value":"0707.0845v2","created_at":"2026-05-18T00:05:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0707.0845","created_at":"2026-05-18T00:05:09Z"},{"alias_kind":"pith_short_12","alias_value":"3FHMFQOGA2L3","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"3FHMFQOGA2L35DDV","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"3FHMFQOG","created_at":"2026-05-18T12:25:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:3FHMFQOGA2L35DDV6AZR7DMKG2","target":"record","payload":{"canonical_record":{"source":{"id":"0707.0845","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.AG","submitted_at":"2007-07-05T18:01:04Z","cross_cats_sorted":[],"title_canon_sha256":"469de84a42e7bcc3e22c92b92e4217e05b9d4a44d0d0d8d224277052932d40ea","abstract_canon_sha256":"e78539493516272266049da63c334eb3775e826c78ef571324cf1ace97d90c7f"},"schema_version":"1.0"},"canonical_sha256":"d94ec2c1c60697be8c75f0331f8d8a36b7ce9eb9444fba1ae7aed6f8bc5c206a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:05:09.990632Z","signature_b64":"S86IwR/GR5rzwI5eCCJYNKd2S7XjSSklxzcClXWLS1LMTg9V6W9Q6NBkhxqGuhGQ73HUBQDsbDa31g8d957KAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d94ec2c1c60697be8c75f0331f8d8a36b7ce9eb9444fba1ae7aed6f8bc5c206a","last_reissued_at":"2026-05-18T00:05:09.990065Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:05:09.990065Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0707.0845","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":"2026-05-18T00:05:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Y6x55ZKIDqPKghBf+LFfvaHYnaSi5uDG5Psf2J2+IgQccfqkOn5wH/ftlnYneHU2CSymPaYvXPOaC20xlborCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T21:11:02.394343Z"},"content_sha256":"686b58420c458ac6161747a05d31a93eb4e57d56f5d4cc4c802d106afb52146f","schema_version":"1.0","event_id":"sha256:686b58420c458ac6161747a05d31a93eb4e57d56f5d4cc4c802d106afb52146f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:3FHMFQOGA2L35DDV6AZR7DMKG2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Logarithmic limit sets of real semi-algebraic sets","license":"","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Daniele Alessandrini","submitted_at":"2007-07-05T18:01:04Z","abstract_excerpt":"This paper is about the logarithmic limit sets of real semi-algebraic sets, and, more generally, about the logarithmic limit sets of sets definable in an o-minimal, polynomially bounded structure. We prove that most of the properties of the logarithmic limit sets of complex algebraic sets hold in the real case. This include the polyhedral structure and the relation with the theory of non-archimedean fields, tropical geometry and Maslov dequantization."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0707.0845","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":"2026-05-18T00:05:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WplCjmGQlrmi2xXlOAooTPjjwrpKJ8eWr7WcVpK+0qYp9SxXOR+Kbm5N0EZwcV/Vk3xxam/HOaxscb9ZhoFICw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T21:11:02.395008Z"},"content_sha256":"8b85bbe6d88341f15a3f8703e042cde124fc8a889ed5675e98345c2fa311afd6","schema_version":"1.0","event_id":"sha256:8b85bbe6d88341f15a3f8703e042cde124fc8a889ed5675e98345c2fa311afd6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3FHMFQOGA2L35DDV6AZR7DMKG2/bundle.json","state_url":"https://pith.science/pith/3FHMFQOGA2L35DDV6AZR7DMKG2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3FHMFQOGA2L35DDV6AZR7DMKG2/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":"2026-05-30T21:11:02Z","links":{"resolver":"https://pith.science/pith/3FHMFQOGA2L35DDV6AZR7DMKG2","bundle":"https://pith.science/pith/3FHMFQOGA2L35DDV6AZR7DMKG2/bundle.json","state":"https://pith.science/pith/3FHMFQOGA2L35DDV6AZR7DMKG2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3FHMFQOGA2L35DDV6AZR7DMKG2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:3FHMFQOGA2L35DDV6AZR7DMKG2","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":"e78539493516272266049da63c334eb3775e826c78ef571324cf1ace97d90c7f","cross_cats_sorted":[],"license":"","primary_cat":"math.AG","submitted_at":"2007-07-05T18:01:04Z","title_canon_sha256":"469de84a42e7bcc3e22c92b92e4217e05b9d4a44d0d0d8d224277052932d40ea"},"schema_version":"1.0","source":{"id":"0707.0845","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0707.0845","created_at":"2026-05-18T00:05:09Z"},{"alias_kind":"arxiv_version","alias_value":"0707.0845v2","created_at":"2026-05-18T00:05:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0707.0845","created_at":"2026-05-18T00:05:09Z"},{"alias_kind":"pith_short_12","alias_value":"3FHMFQOGA2L3","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"3FHMFQOGA2L35DDV","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"3FHMFQOG","created_at":"2026-05-18T12:25:54Z"}],"graph_snapshots":[{"event_id":"sha256:8b85bbe6d88341f15a3f8703e042cde124fc8a889ed5675e98345c2fa311afd6","target":"graph","created_at":"2026-05-18T00:05:09Z","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 paper is about the logarithmic limit sets of real semi-algebraic sets, and, more generally, about the logarithmic limit sets of sets definable in an o-minimal, polynomially bounded structure. We prove that most of the properties of the logarithmic limit sets of complex algebraic sets hold in the real case. This include the polyhedral structure and the relation with the theory of non-archimedean fields, tropical geometry and Maslov dequantization.","authors_text":"Daniele Alessandrini","cross_cats":[],"headline":"","license":"","primary_cat":"math.AG","submitted_at":"2007-07-05T18:01:04Z","title":"Logarithmic limit sets of real semi-algebraic sets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0707.0845","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":"sha256:686b58420c458ac6161747a05d31a93eb4e57d56f5d4cc4c802d106afb52146f","target":"record","created_at":"2026-05-18T00:05:09Z","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":"e78539493516272266049da63c334eb3775e826c78ef571324cf1ace97d90c7f","cross_cats_sorted":[],"license":"","primary_cat":"math.AG","submitted_at":"2007-07-05T18:01:04Z","title_canon_sha256":"469de84a42e7bcc3e22c92b92e4217e05b9d4a44d0d0d8d224277052932d40ea"},"schema_version":"1.0","source":{"id":"0707.0845","kind":"arxiv","version":2}},"canonical_sha256":"d94ec2c1c60697be8c75f0331f8d8a36b7ce9eb9444fba1ae7aed6f8bc5c206a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d94ec2c1c60697be8c75f0331f8d8a36b7ce9eb9444fba1ae7aed6f8bc5c206a","first_computed_at":"2026-05-18T00:05:09.990065Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:05:09.990065Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"S86IwR/GR5rzwI5eCCJYNKd2S7XjSSklxzcClXWLS1LMTg9V6W9Q6NBkhxqGuhGQ73HUBQDsbDa31g8d957KAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:05:09.990632Z","signed_message":"canonical_sha256_bytes"},"source_id":"0707.0845","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:686b58420c458ac6161747a05d31a93eb4e57d56f5d4cc4c802d106afb52146f","sha256:8b85bbe6d88341f15a3f8703e042cde124fc8a889ed5675e98345c2fa311afd6"],"state_sha256":"d230831b5efb23fa9bf03c9a5e549e04739fd411577ca6ff1607242c9238bd75"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PWgkUFofECNYfRbsfFD0AxfdOOv3fjLxaak1Oc8jlNWmYEKxNL5lAcce7apJcAQHLpQ39/beHnJk6Xyjt3yWBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T21:11:02.397944Z","bundle_sha256":"cf1ac752004c21c412a4ac9abc2e396eb2f716501684f0aec2c012f7846e9881"}}